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代数

这是什么代数恒等式?

1 + \压裂{2}{2}+ \压裂{3}{4}+ \压裂{4}{8}+ \压裂{5}{16}+ \ cdots = 4

1 + \压裂{1}{2}+ \压裂{1}{4}+ \压裂{1}{8}+ \ cdots = 2

1 + \压裂{1}{2 ^ 2}+ \压裂{1}{3 ^ 2}+ \压裂{1}{4 ^ 2}+ \ cdots = \压裂{\π^ 2}{6}

1 + \压裂{1}{2}+ \压裂{1}{3}+ \压裂{1}{4}+ \压裂{1}{5}+ \ cdots = \ infty