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Let n is a rational number and x is a re...

Let n is a rational number and x is a real number such that |x|lt1, then
`(1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . .`
This can be used to find the sm of different series.
Q. The sum of the series
`1+(1)/(3^(2))+(1*4)/(1*2)*(1)/(3^(4))+(1*4*7)/(1*2*3)*(1)/(3^(6))+ . . . . `is

A

`sqrt((3)/(2))`

B

`((3)/(2))^(1//3)`

C

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

D

`((2)/(3))^(1//3)`

Text Solution

Verified by Experts

The correct Answer is:
B
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