伸缩系列 - 总和据/h1>
已经有一个帐户?据一种href="//www.parkandroid.com/account/login/?next=/wiki/telescoping-series/" class="ax-click" data-ax-id="clicked_signup_modal_login" data-ax-type="link">这里登录。据/a>
测验据/h4>
相关......据/h4>
- 代数据/span>>据/span>
- 结石据/span>>据/span>
- 量化融资据/span>>据/span>
一种据strong>伸缩系列据/strong>是每个学期的系列据span class="katex">
你据/span>K.据/span>可以写成据span class="katex">
你据/span>K.据/span>=据/span>T.据/span>K.据/span>-据/span>T.据/span>K.据/span>+据/span>1据/span>有些系列据span class="katex">
T.据/span>K.据/span>。这是代数的具有挑战性的子部分,要求求解器在一系列分数中寻找模式,并使用大量的逻辑思维。这些图案通常不会导致质量消除,使得用手解决问题。一些模式比其他模式更难找到。经常,据一种href="//www.parkandroid.com/wiki/partial-fractions/" class="wiki_link" title="部分分数" target="_blank">部分分数据/a>这里使用的方式在稍后演示。据/p>
这样的系列的好处是它允许我们轻松加起来,因为据/p>
你据/span>1据/span>+据/span>你据/span>2据/span>+据/span>你据/span>3.据/span>+据/span>⋯据/span>+据/span>你据/span>N据/span>=据/span>(据/span>T.据/span>1据/span>-据/span>T.据/span>2据/span>)据/span>+据/span>(据/span>T.据/span>2据/span>-据/span>T.据/span>3.据/span>)据/span>+据/span>(据/span>T.据/span>3.据/span>-据/span>T.据/span>4.据/span>)据/span>+据/span>⋯据/span>+据/span>(据/span>T.据/span>N据/span>-据/span>T.据/span>N据/span>+据/span>1据/span>)据/span>=据/span>T.据/span>1据/span>-据/span>T.据/span>N据/span>+据/span>1据/span>。据/span> 观察到大部分据span class="katex">
T.据/span>K.据/span>条款在其他括号中与他们的对手取消,因此我们只留下来据span class="katex">
T.据/span>1据/span>-据/span>T.据/span>N据/span>+据/span>1据/span>。这与可折叠的望远镜相当,其中长峡谷容易缩回到适合您口袋的小仪器中。据/p>
当你通过工作据一种href="//www.parkandroid.com/problems/telescoping-series-1-find-the-next-term/">Arron的望远镜系列调查据/a>,你会意识到这系列据span class="katex">
你据/span>K.据/span>=据/span>K.据/span>(据/span>K.据/span>+据/span>1据/span>)据/span>1据/span>和条款据span class="katex">
T.据/span>K.据/span>=据/span>K.据/span>1据/span>, 我们有据span class="katex">
你据/span>K.据/span>=据/span>T.据/span>K.据/span>-据/span>T.据/span>K.据/span>+据/span>1据/span>自从据/p>
K.据/span>1据/span>-据/span>K.据/span>+据/span>1据/span>1据/span>=据/span>K.据/span>(据/span>K.据/span>+据/span>1据/span>)据/span>K.据/span>+据/span>1据/span>-据/span>K.据/span>(据/span>K.据/span>+据/span>1据/span>)据/span>K.据/span>=据/span>K.据/span>(据/span>K.据/span>+据/span>1据/span>)据/span>1据/span>。据/span> 因此,我们有我们的伸缩系列。这让我们得出结论据/p>
一世据/span>=据/span>1据/span>σ.据/span>N据/span>一世据/span>(据/span>一世据/span>+据/span>1据/span>)据/span>1据/span>=据/span>1据/span>1据/span>-据/span>N据/span>+据/span>1据/span>1据/span>。据/span> 特别是,自从据span class="katex">
N据/span>+据/span>1据/span>1据/span>接近0据span class="katex">
N据/span>变大,我们得到了据/p>
一世据/span>=据/span>1据/span>σ.据/span>∞据/span>一世据/span>(据/span>一世据/span>+据/span>1据/span>)据/span>1据/span>=据/span>1据/span>。据/span> 评估据span class="katex">
4.据/span>1据/span>+据/span>2据/span>8.据/span>1据/span>+据/span>7.据/span>0.据/span>1据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>0.据/span>0.据/span>1据/span>。据/p>
观察我们可以将此表达写为据span class="katex">
1据/span>×据/span>4.据/span>1据/span>+据/span>4.据/span>×据/span>7.据/span>1据/span>+据/span>7.据/span>×据/span>1据/span>0.据/span>1据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>×据/span>1据/span>0.据/span>0.据/span>1据/span>。据/p>
然后有一种方法可以让这一部分取消本身,这是据/p>
1据/span>×据/span>4.据/span>1据/span>+据/span>4.据/span>×据/span>7.据/span>1据/span>+据/span>7.据/span>×据/span>1据/span>0.据/span>1据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>×据/span>1据/span>0.据/span>0.据/span>1据/span>=据/span>3.据/span>1据/span>(据/span>1据/span>×据/span>4.据/span>4.据/span>-据/span>1据/span>+据/span>4.据/span>×据/span>7.据/span>7.据/span>-据/span>4.据/span>+据/span>7.据/span>×据/span>1据/span>0.据/span>1据/span>0.据/span>-据/span>7.据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>×据/span>1据/span>0.据/span>0.据/span>1据/span>0.据/span>0.据/span>-据/span>9.据/span>7.据/span>)据/span>=据/span>3.据/span>1据/span>(据/span>1据/span>1据/span>-据/span>4.据/span>1据/span>+据/span>4.据/span>1据/span>-据/span>7.据/span>1据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>1据/span>-据/span>1据/span>0.据/span>0.据/span>1据/span>)据/span>=据/span>3.据/span>1据/span>(据/span>1据/span>-据/span>1据/span>0.据/span>0.据/span>1据/span>)据/span>=据/span>3.据/span>1据/span>(据/span>1据/span>0.据/span>0.据/span>9.据/span>9.据/span>)据/span>=据/span>1据/span>0.据/span>0.据/span>3.据/span>3.据/span>。据/span>□据/span> 评估据span class="katex">
1据/span>
+据/span>2据/span>
1据/span>+据/span>2据/span>
+据/span>3.据/span>
1据/span>+据/span>3.据/span>
+据/span>4.据/span>
1据/span>+据/span>⋯据/span>+据/span>9.据/span>9.据/span>
+据/span>1据/span>0.据/span>0.据/span>
1据/span>。据/span> 通过分母的缀合物乘以每个分数的分子和分母。然后,例如,第一个术语简化了据/p>
1据/span>
+据/span>2据/span>
1据/span>⋅据/span>2据/span>
-据/span>1据/span>
2据/span>
-据/span>1据/span>
=据/span>2据/span>
-据/span>1据/span>
。据/span> 如果您继续为每次连续分数执行此操作,那么您将继续获得据span class="katex">
1据/span>在分母中获得据/p>
(据/span>2据/span>
-据/span>1据/span>
)据/span>+据/span>(据/span>3.据/span>
-据/span>2据/span>
)据/span>+据/span>(据/span>4.据/span>
-据/span>3.据/span>
)据/span>+据/span>⋯据/span>。据/span> 像望远镜一样,这一切都可以折叠,最后一分的分数简化了据span class="katex">
1据/span>0.据/span>0.据/span>
-据/span>9.据/span>9.据/span>
。因为它是据span class="katex">
9.据/span>9.据/span>
这将被取消,给定的表达式等于据/p>
1据/span>0.据/span>0.据/span>
-据/span>1据/span>
=据/span>1据/span>0.据/span>-据/span>1据/span>=据/span>9.据/span>。据/span>□据/span>
评估据span class="katex">
N据/span>=据/span>1据/span>σ.据/span>2据/span>0.据/span>1据/span>5.据/span>N据/span>2据/span>+据/span>3.据/span>N据/span>+据/span>2据/span>1据/span>。据/p>
对于这种类型的问题,你需要一些知识据一种T.一种rget="_blank" rel="nofollow" href="//www.parkandroid.com/wiki/partial-fractions-linear-factors/">部分分数据/a>。据/p>
改写据span class="katex">
N据/span>2据/span>+据/span>3.据/span>N据/span>+据/span>2据/span>1据/span>在形式据span class="katex">
N据/span>+据/span>1据/span>一种据/span>+据/span>N据/span>+据/span>2据/span>B.据/span>。然后我们可以这么说据span class="katex">
一种据/span>(据/span>N据/span>+据/span>2据/span>)据/span>+据/span>B.据/span>(据/span>N据/span>+据/span>1据/span>)据/span>=据/span>1据/span>。据/span> 弄清楚值的简单方法据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是插入一些简单的数字。例如,让据span class="katex">
N据/span>=据/span>-据/span>2据/span>。然后我们得到据span class="katex">
0.据/span>一种据/span>-据/span>B.据/span>=据/span>1据/span>, 所以据span class="katex">
B.据/span>=据/span>-据/span>1据/span>。如果我们让我们据span class="katex">
N据/span>=据/span>-据/span>1据/span>,然后我们得到据span class="katex">
一种据/span>+据/span>0.据/span>B.据/span>=据/span>1据/span>, 所以据span class="katex">
一种据/span>=据/span>1据/span>。我们的部分分数分解产生了据span class="katex">
N据/span>2据/span>+据/span>3.据/span>N据/span>+据/span>2据/span>1据/span>=据/span>N据/span>+据/span>1据/span>1据/span>-据/span>N据/span>+据/span>2据/span>1据/span>。据/p>
现在,我们有据span class="katex">
N据/span>=据/span>1据/span>σ.据/span>2据/span>0.据/span>1据/span>5.据/span>[据/span>N据/span>+据/span>1据/span>1据/span>-据/span>N据/span>+据/span>2据/span>1据/span>]据/span>。这意味着我们有据/p>
2据/span>1据/span>-据/span>3.据/span>1据/span>+据/span>3.据/span>1据/span>-据/span>4.据/span>1据/span>+据/span>4.据/span>1据/span>-据/span>5.据/span>1据/span>+据/span>⋯据/span>+据/span>2据/span>0.据/span>1据/span>5.据/span>1据/span>-据/span>2据/span>0.据/span>1据/span>6.据/span>1据/span>+据/span>2据/span>0.据/span>1据/span>6.据/span>1据/span>-据/span>2据/span>0.据/span>1据/span>7.据/span>1据/span>。据/span> 请注意如何取消一系列术语,如折叠望远镜。据/p>
这片叶子据/p>
2据/span>1据/span>-据/span>2据/span>0.据/span>1据/span>7.据/span>1据/span>=据/span>4.据/span>0.据/span>3.据/span>4.据/span>2据/span>0.据/span>1据/span>5.据/span>。据/span>□据/span> 让据span class="katex">
F据/span>N据/span>是斐波纳契序列据span class="katex">
F据/span>0.据/span>=据/span>F据/span>1据/span>=据/span>1据/span>和据span class="katex">
F据/span>N据/span>+据/span>2据/span>=据/span>F据/span>N据/span>+据/span>1据/span>+据/span>F据/span>N据/span>对所有人据span class="katex">
N据/span>≥据/span>0.据/span>。据/p>
证明据span class="katex">
K.据/span>=据/span>1据/span>σ.据/span>N据/span>F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>+据/span>1据/span>1据/span>据据/span>1据/span>对所有人据span class="katex">
N据/span>≥据/span>1据/span>。据/p>
对所有人据span class="katex">
K.据/span>≥据/span>1据/span>, 我们有据/p>
F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>+据/span>1据/span>1据/span>=据/span>F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>F据/span>K.据/span>+据/span>1据/span>F据/span>K.据/span>=据/span>F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>F据/span>K.据/span>+据/span>1据/span>F据/span>K.据/span>+据/span>1据/span>-据/span>F据/span>K.据/span>-据/span>1据/span>=据/span>F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>1据/span>-据/span>F据/span>K.据/span>F据/span>K.据/span>+据/span>1据/span>1据/span>。据/span> 因此,我们有我们的伸缩系列。这让我们得出结论据/p>
K.据/span>=据/span>1据/span>σ.据/span>N据/span>F据/span>K.据/span>-据/span>1据/span>F据/span>K.据/span>+据/span>1据/span>1据/span>=据/span>F据/span>0.据/span>F据/span>1据/span>1据/span>-据/span>F据/span>N据/span>F据/span>N据/span>+据/span>1据/span>1据/span>=据/span>1据/span>-据/span>F据/span>N据/span>F据/span>N据/span>+据/span>1据/span>1据/span>据据/span>1据/span>。据/span>□据/span>
2据/span>2据/span>-据/span>1据/span>1据/span>+据/span>4.据/span>2据/span>-据/span>1据/span>1据/span>+据/span>6.据/span>2据/span>-据/span>1据/span>1据/span>+据/span>8.据/span>2据/span>-据/span>1据/span>1据/span>+据/span>⋯据/span>+据/span>1据/span>0.据/span>0.据/span>0.据/span>2据/span>-据/span>1据/span>1据/span> 上面的总和的价值可以表示为据span class="katex">
B.据/span>一种据/span>那据/span>在哪里据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是coprime正整数。找到价值据span class="katex">
一种据/span>+据/span>B.据/span>。据/p>
2据/span>1据/span>
+据/span>1据/span>2据/span>
1据/span>+据/span>3.据/span>2据/span>
+据/span>2据/span>3.据/span>
1据/span>+据/span>4.据/span>3.据/span>
+据/span>3.据/span>4.据/span>
1据/span>+据/span>⋯据/span>+据/span>2据/span>4.据/span>2据/span>3.据/span>
+据/span>2据/span>3.据/span>2据/span>4.据/span>
1据/span>+据/span>2据/span>5.据/span>2据/span>4.据/span>
+据/span>2据/span>4.据/span>2据/span>5.据/span>
1据/span>=据/span>还是据/span>
N据/span>=据/span>1据/span>σ.据/span>2据/span>0.据/span>1据/span>6.据/span>1据/span>3.据/span>+据/span>2据/span>3.据/span>+据/span>3.据/span>3.据/span>+据/span>⋯据/span>+据/span>N据/span>3.据/span>1据/span>+据/span>2据/span>+据/span>3.据/span>+据/span>⋯据/span>+据/span>N据/span> 如果此总和的值是据span class="katex">
B.据/span>一种据/span>, 在哪里据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是coprime积极整数,找到据span class="katex">
一种据/span>+据/span>B.据/span>。据/span>
4.据/span>3.据/span>+据/span>2据/span>8.据/span>3.据/span>+据/span>7.据/span>0.据/span>3.据/span>+据/span>1据/span>3.据/span>0.据/span>3.据/span>+据/span>⋯据/span>+据/span>9.据/span>7.据/span>0.据/span>0.据/span>3.据/span>=据/span>还是据/span>
N据/span>=据/span>3.据/span>σ.据/span>∞据/span>(据/span>3.据/span>N据/span>)据/span>1据/span>=据/span>(据/span>3.据/span>3.据/span>)据/span>1据/span>+据/span>(据/span>3.据/span>4.据/span>)据/span>1据/span>+据/span>(据/span>3.据/span>5.据/span>)据/span>1据/span>+据/span>(据/span>3.据/span>6.据/span>)据/span>1据/span>+据/span>⋯据/span>=据/span>还是据/span>
8.据/span>1据/span>(据/span>1据/span>⋅据/span>2据/span>⋅据/span>3.据/span>⋅据/span>4.据/span>1据/span>+据/span>2据/span>⋅据/span>3.据/span>⋅据/span>4.据/span>⋅据/span>5.据/span>1据/span>+据/span>3.据/span>⋅据/span>4.据/span>⋅据/span>5.据/span>⋅据/span>6.据/span>1据/span>+据/span>4.据/span>⋅据/span>5.据/span>⋅据/span>6.据/span>⋅据/span>7.据/span>1据/span>+据/span>⋯据/span>)据/span> 找到上面表达式的值。据/p>
一种据/span>N据/span>B.据/span>N据/span>C据/span>N据/span>=据/span>1据/span>+据/span>6.据/span>(据/span>N据/span>-据/span>1据/span>)据/span>=据/span>1据/span>+据/span>2据/span>1据/span>(据/span>N据/span>-据/span>1据/span>)据/span>=据/span>2据/span>0.据/span>2据/span>+据/span>1据/span>0.据/span>2据/span>(据/span>N据/span>-据/span>1据/span>)据/span> 鉴于上述情况,什么是值据/p>
2据/span>!!据/span>1据/span>+据/span>3.据/span>!!据/span>1据/span>+据/span>4.据/span>!!据/span>一种据/span>1据/span>+据/span>5.据/span>!!据/span>B.据/span>1据/span>+据/span>6.据/span>!!据/span>C据/span>1据/span>+据/span>7.据/span>!!据/span>一种据/span>2据/span>+据/span>8.据/span>!!据/span>B.据/span>2据/span>+据/span>9.据/span>!!据/span>C据/span>2据/span>+据/span>1据/span>0.据/span>!!据/span>一种据/span>3.据/span>+据/span>1据/span>1据/span>!!据/span>B.据/span>3.据/span>+据/span>1据/span>2据/span>!!据/span>C据/span>3.据/span>+据/span>⋯据/span>还是据/span>
澄清据/strong>:分数的分母遵循二次函数。据/p>