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The value of sum(r=1)^(n) (-1)^(r+1)(""^...

The value of `sum_(r=1)^(n) (-1)^(r+1)(""^(n)C_(r))/(r+1)` is equal to

A

(a) `-1/(n+1)`

B

(b) `-(1)/(n)`

C

(c) `(1)/(n+1)`

D

(d) `(n)/(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(r=1)overset(n)sum(-1)^(r+1)(.^(n)C_(r))/((r+1))= (1)/(n+1)underset(r=1)overset(n)sum(-1)^(r+1).^(n+1)C_(r+1)`
`= 1/(n+1)(0-1+(n+1))= (n)/(n+1)`
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