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