Q90 / 170 · Manipal (MET) 2021 · Mathematics

$\sum_{n=1}^{\infty} \frac{(-1)^n}{n+1}$ is equal to

  • A
    $e^{-1}$
  • Correct answer
    B
    $\log 2-1$
  • C
    1
  • D
    0

Solution

$\begin{aligned} \sum_{n=1}^{\infty} \frac{(-1)^n}{n+1} & =-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots \infty \\ & =1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots \infty-1 \\ & =\log 2-1\end{aligned}$

Hence, the correct answer is option: 'B'.

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