部分分数:3级挑战在线练习问题| Brilliant

$\压裂{1}{2 !} + \压裂{2}{3 !} + \压裂{3}{4 !} + \压裂{4}{5 !} + \cdots = \ ?$

$1 + \压裂{1}{\颜色# 3 d99f6}{2} + \压裂{1}{{# 3 d99f6} \颜色6}+ \压裂{1}{\颜色{# 3 d99f6}{12}} + \压裂{1}{\颜色{# 3 d99f6} {20}} + \ ldots = {teal} \ \颜色?$

3.

4

1

\ infty

2

$\ \ displaystyle \大sum_ {n = 1} ^ {\ infty} \ dfrac {1} {n ^ 2 + 3 n + 2} = \ ?$

$\压裂{1}{(x - 1) (x - 2)} + \压裂{1}{(x - 2)(3)} + \压裂{1}{(- 3)(* 4)}= \压裂{1}{6}$

的所有实数的和是多少 $x$ 满足上面的方程?

$大\ \ sqrt [3] {\ sqrt {32}} \ sqrt [4] {\ sqrt [3] {32}} \ sqrt [5] {\ sqrt [4] {32}} \ cdots \ sqrt [10] {\ sqrt [9] {32}} = \ ?$

部分分数:3级挑战