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If (1 +x+x^2)^n=sum(r=0)^(2n) ar x^r , t...

If `(1 +x+x^2)^n=sum_(r=0)^(2n) a_r x^r` , then prove that `a_r=a_(2n-r)`

A

`n+1`

B

`r+1`

C

`n+r+1`

D

`n+r`

Text Solution

Verified by Experts

The correct Answer is:
C
Coeff. `X^(3r)` in `[(1+x+x^(2))^(n)(1-x)^(n)]`
`implies` coeff. of `x^(3r)` in `[(a_(0)+a_(1)x+…a_(2)x^(2n))(n_(c_(0))-n_(c_(1)) xx……)]`
`.^(n)C_(r)`
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