Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If S1, S2, S3, ... , Sn are the sums of infinite G.P.s. whose first terms ars 1, 2, 3, ..., n and whose common ratios are 1/2, 1/3 , 1/4, ...1/n+1 respectively, then ∑i = 1nSi =

(1) n(n+3)/2

(2) n(n+4)/2

(3) n(n-3)/2

(4) n(n+1)/2

Solution:

i = 1nSi = ∑i = 1na/(1-r)

S1 = 1/(1-½) = 2

S2 = 2/(1-1/3) = 3

S3 = 3/(1-¼) = 4

Sn = n+1

i = 1na/(1-r) = 2+3+4+…..(n+1)

= (n/2)(4+(n-1)1)

= (n/2)(3+n)

= n(n+3)/2

Hence option (1) is the answer.

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