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 the sum of n terms of sequence S_(n)=(n)/(n+1)

If S_(n), be the sum of n terms of an A.P; the value of S_(n)-2S_(n-1)+S_(n-2), is

If S_(n) is the sum of a G.P. to n terms of which r is the common ratio, then : (r-1)*(d)/(dr)(S_(n))+nS_(n-1)=

Let S_(n) be the sum of n terms of an A.P. Let us define a_(n)=(S_(3n))/(S_(2n)-S_(n)) then sum_(r=1)^(oo)(a_(r))/(2^(r-1)) is

S_(r) denotes the sum of the first r terms of an AP.Then S_(3d):(S_(2n)-S_(n)) is -

If for a sequence {a_(n)},S_(n)=2n^(2)+9n , where S_(n) is the sum of n terms, the value of a_(20) is

If sum of n terms of a sequence is given by S_(n)=3n^(2)-5n+7&t_(r) represents its r^(th) term then

If S_(n) denotes the sum of first n terms of an A.P., then (S_(3n)-S_(n-1))/(S_(2n)-S_(n-1)) is equal to

Suppose a series of n terms given by S_(n)=t_(1)+t_(2)+t_(3)+ . . .. +t_(n) then S_(n-1)=t_(1)+t_(2)+t_(3)+ . . . +t_(n-1),nge1 subtracting we get S_(n)-S_(n-1)=t_(n),nge2 surther if we put n=1 is the first sum then S_(1)=t_(1) thus w can write t_(n)=S_(n)-S_(n-1),nge2 and t_(1)=S_(1) Q. if the sum of n terms of a series a.2^(n)-b then the sum sum_(r=1)^(infty)(1)/(t_(r)) is