If \((1/2^1) + (1/2^2) + (1/2^3)....(1/2^{10})=1/k\), then what is the value of k?

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Question

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 16 (Held On: 9 March 2018)

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Answer 1

Given:

(1/2¹) + (1/2²) + (1/2³) + ……… + (1/2¹⁰) = 1/k

Formula used:

Sum of G.P = a(1 – rⁿ)/(1 – r)

Calculation:

(1/2¹) + (1/2²) + (1/2³) + ……… + (1/2¹⁰) = 1/k

Left hand side of the above series in GP and common ratio = ½

∴ Sum of the given series = [1(1 – rⁿ)/(1- r)]

⇒ ½ × [(1 – (½)¹⁰]/ (1-1/2)

⇒ ½ × [1 – 1/1024]/ (1/2)

⇒ 1023/1024 = 1/k

⇒ k = 1024/1023

∴ The correct answer is 1024/1023.

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