JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

Define

a_n=n^2+20

for

n=1,2,3, \ldots

. Let

d_n

be the greatest common divisor of

a_n

and

a_{n+1}

and

d

be the least common multiple of

d_n

for

n=1,2,3, \ldots

. Then the infinite sum of the series

d+\frac{d}{4}+\frac{d}{4^2}+\frac{d}{4^3}+\cdots

View answer and explanation

Correct option: C

108

Option C (108) is correct because it is the sum of the infinite geometric series with first term d=81 and common ratio 1/4.

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