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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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\sum_{n=1}^{\infty} \left( rac{1}{n + 1} - rac{1}{n + 2}
This is a telescoping series. Writing the partial sum \( S_N \):
S_N = \left( rac{1}{2} - rac{1}{3}
ight) + \left( rac{1}{3} - rac{1}{4}
ight) + \cdots + \left( rac{1}{N+1} - rac{1}{N+2}
ight) = rac{1}{2} - rac{1}{N+2}
As \( N o \infty \), \( rac{1}{N+2} o 0 \), so:
\lim_{N o \infty} S_N = rac{1}{2}
The series converges to \( rac{1}{2} \).
oxed{ ext{The series converges to } rac{1}{2}}

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