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Home / ight) = rac{1}{2} - rac{1}{N+2}

ight) = rac{1}{2} - rac{1}{N+2}

February 22, 2026

ight) = rac{1}{2} - rac{1}{N+2}

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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}
As \( N o \infty \), \( rac{1}{N+2} o 0 \), so:
\lim_{N o \infty} S_N = rac{1}{2}
The series converges to \( rac{1}{2} \).

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