Question

If `(1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n)`.
The value of `a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n)` when `p=-3` and `n in` even is
A. `n`
B. `2n-1`
C. `2n-2`
D. `2n`

Answer 1

Correct Answer - D
`(d)` `a_(1)+5a_(2)+9a_(3)+…+(4n-1)a_(2n)=sum_(r=1)^(2n)(2r-1)a_(r )`
`s=2sum_(r=1)^(2n)ra_(r )-sum_(r=1)^(2n)a_(r )`
`=2n(p+2)-((p+2)^(n)-1)`
`=(2n-1)(p+2)^(n)+1`
now `p=-3` and `n in` even
`:.s=(2n-1)+1=2n`