Let `S_k ,k=1,2, ,100 ,` denotes thesum of the infinite geometric series whose first term s `(k-1)/(k !)` and the common ratio is `1/k` , then the value of `(100^2)/(100 !)+sum_(k=1)^(100)(k^2-3k+1)S_k` is _______.

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

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....

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

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

Let S_(K) be the sum of an infinte G.P. series whose first term is K and common ratio is (K)/(K+1)(Kgt0) . Then the value of sum_(K=1)^(oo)((-1)^(K))/(S_(K)) is equal to

Find the value of 2551 S where S = sum_(k=1)^(50) k/(k^(4)+k^(2)+1)

If sum_(k=1)^(n)k=210, find the value of sum_(k=1)^(n)k^(2).