Let `S_(k)` denote sum of infinite geometric series `(K=1,2,3,.......),` where first term is `(k^(2)-1)` and common ratio is `(1)/(K),` then the unit digit of the sum `(sum_(k=1)^(oo)(S_(k))/(2^(k-1))),` is

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

Let s_k, k=1,2,3,…,100 denote the sum of the infinite geometric series whose first term is (k-1)/|___k and the common ratio is 1/k . Then, the value of is

Find the sum sum_(k=1) (""^nC_(2k-1))/(2k)

Let S_(k) , be the sum of an infinite geometric series whose first term is kand common ratio is (k)/(k+1)(kgt0) . Then the value of sum_(k=1)^(oo)(-1)^(k)/(S_(k)) is equal to

The Sum sum_(K=1)^(20)K(1)/(2^(K)) is equal to.

Let S_(k) , where k = 1,2 ,....,100, denotes the sum of the infinite geometric series whose first term is (k -1)/(k!) and the common ratio is (1)/(k) . Then, the value of (100^(2))/(100!) +sum_(k=2)^(100) | (k^(2) - 3k +1) S_(k)| is....

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

The sum sum_(k=1)^(n)k(k^(2)+k+1) is equal to

The sum sum_(k=1)^oocot^(-1)(2k^2) equals

The sum sum_(k=1)^(100)(k)/(k^(4)+k^(2)+1) is equal to