If `sum_(r=1)^n r^4= a_n then sum_(r=1)^n(2r-1)^4)=` (A) `a_(2n)+a_n` (B) `a_(2n)-a_n` (C) `a_(2n)-16a_n` (D) `a_(2n)+16b_n`

If a_n=sum_(r=0)^n1/(nC_r), then sum_(r=0)^n r/(nC_r) equals

If a_n=n/((n+1)!) then find sum_(n=1)^50 a_n

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

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 , then (a) b_(n) = 1+a_(n) (b) b_(n) = (-1)^(n)xxa_(n) (c) b_(n) = (-1)^(n-1) xxa_(n) (d) b_(n) + 1 = a_(n)

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If a_n = n (n!) , then sum_(r=1)^100 a_r is equal to

If S_(n)=sum_(r=1)^(n) a_(r)=(1)/(6)n(2n^(2)+9n+13) , then sum_(r=1)^(n)sqrt(a_(r)) equals

If a_1, a_2, a_3, ,a_(2n+1) are in A.P., then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_(2n)-a_2)/(a_(2n)+a_2)++(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to a. (n(n+1))/2xx(a_2-a_1)/(a_(n+1)) b. (n(n+1))/2 c. (n+1)(a_2-a_1) d. none of these

Find a_(1) and a_(9) if a_(n) is given by a_(n) = (n^(2))/(n+1)

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)