If `S_n = 1+1/2 + 1/2^2+...+1/2^(n-1) and 2-S_n < 1/100,` then the least value of `n` must be :

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

If S_ (n) = (n* ( 2 n^ 2 + 9 n + 13 ))/ 6 ( S_ (n) = sum of first n terms of the sequence) then the value of ∑_ (i = 1)^(oo) 1/ ( r √ (S_ r − S_ (r − 1))

If S=sum_(n=2)^oo (3n^2+1)/(n^2-1)^3 then 9/S=

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

If S_(1),S_(2),S_(3),"…….",S_(2n) are the same of infinite geometric series whose first terms are respectively 1 , 2, 3,"…….", 2n and common ratio are respectively. 1/2, 1/3, '…..". (1)/(2n+1) .Find the value of S_(1)^(2) + S_(2)^(2) + "……" + S_(2n-1)^(2) .