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The series \(\Large \sum\limits_{n=1}^{\infty}\left[ (-1)^{2}/(2n-1) \right]\) is

A) convergent
B) divergent
C) unbounded
D) none of these

Correct Answer:

A) convergent

Description for Correct answer:
Then \(n^{th}\) term \(a_{n}=\)\(\Large\frac{(-1)^{n}}{2n-1}\)

\(\Large \lim\limits_{n\rightarrow \infty}a_{n}=\lim\limits_{n\rightarrow \infty}\begin{vmatrix}\frac{(-1)^{n}}{2n-1}\end{vmatrix}=0\)

\(\Rightarrow \{|a_{n}\}\}\) is a conbergent sequence.

\(\Rightarrow \sum |a_{n}|\) is convergent.

\(\Rightarrow \sum a_{n}\) is convergent and converges to zero.

Part of solved Real Analysis questions and answers : >> Elementary Mathematics >> Real Analysis

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