`T_(k) = K ^(3) + 3 ^(k) ,` then find `sum_(k =1) ^( n ) T _(k).`

If Delta_(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " then " sum_(k=1)^(n) Delta_(k) is equal to

If n is a positive integer and C_(k)=""^(n)C_(k) , then the value of sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2) is :

Find the sum, sum_(k=1) ^(20) (1+2+3+.....+k)

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

Evaluate sum_(k=1)^(11)(2+3^k)

Find the value off sum_(k=1)^10(2+3^k)

If a,b in R^(+) then find Lim_(nrarroo) sum_(k=1)^(n) ( n)/((k+an)(k+bn)) is equal to

If a_(K)=(1)/(K(K+1)) for K=1, 2, 3....n , then (sum_(K=1)^(n)a_(K))^(2)=

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

If I_(n) = |(1,k,k),(2n,k^(2) + k + 1,k^(2) + k),(2n -1,k^(2) ,k^(2) + k +1)| and sum_(n=1)^(k) I_(n) = 72 , then k =