" (5) Evaluate "sum_(k=1)^(n)(2^(k)+3^(k-1))

sum_(k=1)^n k^3=

Find sum_(k=1)^(n)(1)/(k(k+1)) .

Evaluate : (i) sum_(n=1)^(10)(2+3^(n))" " (ii) sum_(k=1)^(n)[2^(k)+3^((k-1))]" " (iii) sum_(n=1)^(8) 5^(n)

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

Evaluate the sum , sum_(k=1)^(n)(1)/(k(k+1)(k+2)……..(k+r)) .

If for n in N,sum_(k=0)^(2n)(-1)^(k)(2nC_(k))^(2)=A, then find the value of sum_(k=0)^(2n)(-1)^(k)(k-2n)(2nC_(k))^(2)

If n is a positive integer and C_(k)=.^(n)C_(k) then find the value of sum_(k=1)^(n)k^(3)*((C_(k))/(C_(k-1)))^(2)

If n is a positive integer SC_(k)=^(n)C_(k), find the value of (sum_(k=1)^(n)(k^(3))/(n(n+1)^(2)*(n+2))((C_(k))/(C_(k)-1))^(2))^(-1)