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If (1+2x+x^(2))^(n) = sum(r=0)^(2n)a(r)x...

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

A

`(.^(n)C_(r))^(2)`

B

`.^(n)C_(r)..^(n)C_(r+1)`

C

`.^(2n)C_(r)`

D

`.^(2n)C_(r+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+2x+x^(2))^(n)=underset(r=0)overset(2n)suma_(r)x^(r)`
or `[(1+x)^(2)]^(n)=underset(r=0)overset(2n)suma_(r)x^(n)`
or `(1+x)^(2n) = underset(r=0)overset(2n)suma_(r)x^(r)`
`underset(r=0)overset(2n)sum.^(2n)C_(r)x^(r) = underset(r=0)overset(2n)suma_(r)x^(r)`
or `a_(r) = .^(2n)C_(r)`
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