If sum of n termsof a sequende is `S_n` then its nth term `t_n=S_n-S_(n-1)`. This relation is vale for all `ngt-1` provided `S_0= 0.` But if `S_!=0`, then the relation is valid ony for `nge2` and in hat cast `t_1` can be obtained by the relation`t_1=S_1.` Also if nth term of a sequence `t_1=S_n-S_(n-1)` then sum of n term of the sequence can be obtained by putting `n=1,2,3,.n` and adding them. Thus `sum_(n=1)^n t_n=S_n-S_0.` if `S_0=0, then sum_(n=1)^n t_n=S_n.` On the basis of above information answer thefollowing questions:If nth term of a sequence is `n/(1+n^2+n^4)` then the sum of its first n terms is (A) `(n^2+n)/(1+n+n^2)` (B) `(n^2-n)/(1+n+n^2)` (C) `(n^2+n)/(1-n+n^2)` (D) `(n^2+n)/(2(1+n+n^2)`

If sum of n terms of a sequence is S_n then its nth term t_n=S_n-S_(n-1) . This relation is valid for all ngt-1 provided S_0= 0. But if S_1=0 , then the relation is valid ony for nge2 and in that case t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_n=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer thefollowing questions: If nth term of a sequence is 1/((n+2)n!) then sum of to infinity of this sequence is (A) 1 (B) 1/2 (C) 1/3 (D) none of these

If sum of n termsof a sequende is S_n then its nth term t_n=S_n-S_(n-1) . This relation is vale for all ngt-1 provided S_0= 0. But if S_!=0 , then the relation is valid ony for nge2 and in hat cast t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_1=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer thefollowing questions: If the sum of n terms of a sequence is 10n^2+7n then the sequence is (A) an A.P. having common difference 20 (B) an A.P. having common difference 7 (C) an A.P. having common difference 27 (D) not an A.P.

If the sum of n terms of a sequence is given by S_(n)=3n^(2)-2nAA n in N , then its 10th term is

If for n sequences S_(n)=2(3^(n)-1) , then the third term is

Find the sum of nth term of this series and S_n denote the sum of its n terms. Then, T_n=[1+(n-1xx2)^2]=(2n-1)^2=4n^2-4n+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 , denotes the sum of n terms of an AP, then the value of (S_(2n)-S_n) is equal to

If S_n the sum of first n terms of an AP is given by 2n^2+n , then find its nth term.

Write the n t h term of an A.P. the sum of whose n terms is S_n .

Write the next three terms of the following sequences: t_1=2, t_n=t_(n-1)-1,ngt=2