Value of `sum_(k=1)^oosum_(r=0)^k1/(3^k)(^k C_r)` is `2/3` b. `4/3` c. `2` d. `1`

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

The sum sum_(k=1)^(20) k (1)/(2^(k)) is equal to

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of int_0^1 ( pi_(r=1)^n (x+r)) (sum_(k=1)^n 1/(x+k)) dx

sum_(k=1)^ook(1-1/n)^(k-1)= a. n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is

Find the value of lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

The value of sum_(k=0)^(n)(i^(k)+i^(k+1)) , where i^(2)= -1 , is equal to

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____" .