Complex Analysis: Theory and Applications · Problem 4.1.5

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · telescoping-series-complex

Problem

Show that ∑n=0∞(1n+1+i−1n+i)=i\displaystyle\sum_{n=0}^{\infty}\left(\frac{1}{n+1+i} - \frac{1}{n+i}\right) = i.

Related theory

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