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If f(x) =1 + nx+ (n(n-1))/(2) x^(2) + (n...

If `f(x) =1 + nx+ (n(n-1))/(2) x^(2) + (n(n-1)(n-2))/(6) x^(3)`
` + ...+x^(n) , "then" f''(1) ` is equal to

A

`n(n-1) 2^(n-1)`

B

`(n-1) 2^(n-1)`

C

`n(n-1) 2^(n-2)`

D

`n(n-1) 2^(n)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `f(x) = 1 + nx + (n(n-1))/(2!) x^(2) + (n(n-1)(n-2))/(3!) x^(3) + ... + x^(n)`
` rArr f(x) = (1 + x)^(n)`
`rArr f'(x) = n (1 + x)^(n-1)`
` rArr f''(x) = n (n-1) (1 + x)^(n-2)`
` rArr f'''(1) = n (n-1) 2^(n-2)` .
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