Let `V_r` denote the sum of the first' ' terms of an arithmetic progression (A.P.) whose first term is'r and the common difference is `(2r-1)`. Let `T_r=V_(r+1)-V_r -2` and `Q_r=T_(r+1) -T_r` for `r=1,2,.......` The sum `V_1+V_2+......+V_n` is

Let Vr denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r – 1). Let T_(r)=V_(r+1)-V_(r)-2 and Q_(r+1)-T_(r) for r=1,2……. The sum V_(1)+V_(2)+….+V_(n) is

Let V_r denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1) . Let T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2 T_r is always (A) an odd number (B) an even number (C) a prime number (D) a composite num,ber

Let V_r denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1) . Let T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2 Which one of the following is a correct statement? (A) Q_1, Q_2, Q_3………….., are in A.P. with common difference 5 (B) Q_1, Q_2, Q_3………….., are in A.P. with common difference 6 (C) Q_1, Q_2, Q_3………….., are in A.P. with common difference 11 (D) Q_1=Q_2=Q_3

Let T_(r) be the rth term of an A.P.whose first term is -1/2 and common difference is 1, then sum_(n)^(n)sqrt(1+T_(r)T_(r+1)T_(r+2)T_(r+3))

Let T_(r) be the r^(th) term of an A.P whose first term is a and common difference is d IF for some integer m,n,T_(m)=(1)/(n) and T_(n)=(1)/(m) then a-d=

Find the sum of firs 100 terms of the series whose general term is given by T_(r)=(r^(2)+1)r! .

If S_(r) denotes the sum of the first r terms of an A.P.then show that (S_(3r)-S_(r-1))/(S_(2r)-S_(2r-1)) is equals