1. Tardigrade
  2. Question
  3. Mathematics
  4. Let S k , k =1,2,3, ldots ldots denote the sum of infinite geometric series whose first term is ( k 2-1) and the common ratio is (1/k). Find the addition of the digits of sum displaystyle∑k=1∞ (Sk/2k-1).

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Q. Let $S _{ k }, k =1,2,3, \ldots \ldots$ denote the sum of infinite geometric series whose first term is $\left( k ^2-1\right)$ and the common ratio is $\frac{1}{k}$. Find the addition of the digits of sum $\displaystyle\sum_{k=1}^{\infty} \frac{S_k}{2^{k-1}}$.

Sequences and Series

Solution:

Correct answer is '5'

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