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1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8x...

`1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) x^(3) + "….."` is equal to

A

`sqrt(2)`

B

`(1)/(sqrt(2))`

C

`sqrt(3)`

D

`(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the given series be identical with
`(1+x)^(n) = 1+nx + (n(n-1))/(1xx2) "…." oo`
`:. nx = 1/4` or `n^(2)x^(2) = 1/16`
Also, `(n(n-1))/(2) x^(2) = 3/(32)`
or `(2n)/(n-1) = ((1)/(16))/((3)/(32)) = 2/3`
or `3n = n-1`
or `2n = - 1`
or `n = - 1/2`
`rArr x = - 1/2`
`:.` Reqired sum `=(1-(1)/(2))^(-1/2)= (1/2)^(-1/2) = (2)^(-1/2) = sqrt(2)`
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