Let `S_(k) = (1+2+3+...+k)/(k)`. If `S_(1)^(2) + s_(2)^(2) +...+S_(10)^(2) = (5)/(12)A`, then A is equal to

If S_(k)=(1+2+...+k)/(k), find the value of S_(1)^(2)+S_(2)^(2)+...+S_(n)^(2)

Let" "S_(k)=( (1 ,k), (0 ,1) ), k in N .Then (S_(2))^(n)(S_(x))^(-1) (where n in N) is equal to: (S_(k))^(-1) denotes the inverse of matrix S_(k)

S_(1)=sum_(k=1)^(n)K,S_(2)=sum_(k=1)^(n)K^(2) and S_(3)=sum_(k=1)^(n)K^(3) then (S_(1)^(4)S_(2)^(2)-S_(2)^(2)S_(3)^(2))/(S_(1)^(2)+S_(3)^(2)) is equal to

If S_k=(1+2+3+...k)/k then find the value of S_1^2+S_2^2+....S_n^2

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) is equal to

Let S _(K) = sum _(r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2r +1))) . Then lim _( k to oo) S _(k) is equal to :

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value