The sum to infinity of the following series 2 + 1/2 + 1/3 + 1/22 + 1/32 + 1/23 + 1/33+...will be

(1) 3

(2) 4

(3) 7/2

(4) 9/2

Solution:

Let S = 2 + 1/2 + 1/3 + 1/22 + 1/32 + 1/23 + 1/33+…

= 2 + (1/2 + 1/22+ 1/23 + ….)+ (1/3 + 1/32 + 1/33+…)

= 2+ (½)/(1-½) + (⅓)/(1-⅓)

= 2 + 1 + ½

= 7/2

Hence option (3) is the answer.

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