Examine the series .

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Examine the series 12+12+122+14+⋯\displaystyle \frac{1}{\sqrt{2}}+\frac12+\frac{1}{2\sqrt{2}}+\frac14+\cdots. (i) Write down the common ratio of the corresponding geometric progression. (ii) State, with reason, whether the infinite series converges or diverges. (iii) Find the sum to infinity, if it exists.

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