The sum of the following infinite series is 2 + 1/2 + 1/3 + 1/4 + 1/8 + 1/9 + 1/16 + 1/27 + ·s

GATE DA 2024 Q4: Sum of an infinite series of powers of 1/2 and 1/3

The sum of the following infinite series is

$2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{8} + \frac{1}{9} + \frac{1}{16} + \frac{1}{27} + \cdots$

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: B (official GATE 2024 final answer key)

Concept used: Sum of geometric series: $\sum_{k\ge1} r^k = \dfrac{r}{1-r}$ for $|r|<1$ .

First step: Split the terms after 2 into powers of $\tfrac{1}{2}$ (sum 1) and powers of $\tfrac{1}{3}$ (sum $\tfrac{1}{2}$ ).

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key