Let `S_k` denotes sum of first k terms of sequence 3,7,11, 15-----------Value of n, if
`40lt6/(n(n+1))sum_(k=1)^nS_klt42` is________

sum_(k=1)^n k^3=

Let S_(n) be the sum to "n" -terms of an arithmetic progression 3,7,11,....... If 40<((6)/(n(n+1))sum_(k=1)^(n)S_(k))<42 , then "n" equals____________

If S_(k) denotes the sum of first k terms of a G.P. Then, S_(n),S_(2n)-S_(n),S_(3n)-S_(2n) are in

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

The value of cot (sum_(n=1)^(23) cot^(-1) (1 + sum_(k=1)^(n) 2k)) is

Let {a_(n)} be an arithmetic sequence with first term 77 and common difference -3. Find the maximum value of sum_(k=1)^(n)a_(k)

If the sum of first 24 terms of a sequence whose n^(th) term is given by t_(n) = 3+(2n)/3 is k , then what is the value of k ?

(1) .Let S_n denote the sum of the first 'n' terms and S_(2n)= 3S_n. Then, the ratio S_(3n):S_n is: (2) let S_1(n) be the sum of the first n terms arithmetic progression 8, 12, 16,..... and S_2(n) be the sum of the first n terms of arithmatic progression 17, 19, 21,....... if S_1(n)=S_2(n) then this common sum is

Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers.Then sum_(r=1)^(n)(S_(r))/(s_(r)) is equal to