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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 sum of different series.
Q. Sum of infinite series
`1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(8)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo` is

A

`2^(1//3)`

B

`4^(1//3)`

C

`8^(1//3)`

D

`2^(1//5)`

Text Solution

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The correct Answer is:
B
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