Question

The value of `Sigma_(r=1)^(n) (a+r+ar)(-a)^r` is equal to
A. `(-1)^n[n+1)a^(n+1)-a]`
B. `(-1)^n(n+1)a^(n+1)`
C. `(-1)^n((n+2)a^(n+1))/2`
D. `(-1)^n(na^n)/(2)`

Answer 1

Correct Answer - B
`T_(r)=r(-a)^(r )+(r+1)a(-a)^(r )`
`=r(-a)^(r )-(r+1)(-a)^(r+1)`
`=v(r )-v(r+1)`
So, `sum_(r=0)^(n)T_(r )=sum_(r=0)^(n)(v(r )-v(r+1))`
`=v_(0)-v_(n+1)`
`=-(n+1)(-a)^(n+1)`