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sum(r=0)^(300)arx^r=(1+x+x^2+x^3)^(100)....

`sum_(r=0)^(300)a_rx^r=(1+x+x^2+x^3)^(100)`. If `a=sum_(r=0)^(300)a_r`, then `sum_(r=0)^(300)ra_r` is equal to

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The correct Answer is:
D
`(1-x)^(n)(1+x)^(n)=underset(r=0)overset(n)suma_(r)x^(r)(1-x)^(n)(1-x)^(n-r)`
or `(1-x+2x)^(n) = underset(r=0)overset(n)suma_(r)x^(r)(1-x)^(n-r)`
or `underset(r=0)overset(n)sum.^(n)C_(r)(1-x)^(n-r)(2x)^(r)=underset(r=0)overset(n)suma_(r)x^(r)(1-x)^(n-r)`
Comparing general term, we get `a_(r) = .^(n)C_(r)2^(r)`.
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