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If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h...

If `(1-x)^(-n)=a_0+a_1x+a_2x^2++a_r x^r+ ,t h e na_0+a_1+a_2++a_r` is equal to
a. `(n(n+1)(n+2)(n+r))/(r !)`
b. `((n+1)(n+2)(n+r))/(r !)`
c. `(n(n+1)(n+2)(n+r-1))/(r !)`
d. none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`a_(0) + a_(1) + a_(2) +"……"+a_(r)`
= Coefficient of `x^(r)` in the product of the two series
= Coefficient of `x^(r)` in `(1-x)^(-n)(1-x)^(-1)`
= Coefficient of `x^(r)` in `(1-x)^(-(n+1))`
`= ((n+1)(n+2)"…."(n+r))/(r!) = .^(n+r)C_(n)`
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