Let `V_(r )` denotes the sum of the first r terms of an arithmetic progression 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

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

If the sum of the first 4 terms of an arithmetic progression is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express 3p+r in terms of q.

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

Write the sum of n term fo a series whose r^(t h) term is: r+2^rdot

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

Let T be the r th term of an A.P. whose first term is a and conmon difference is d . If for some positive integers m ,n, T_(n)= (1)/(m) , T_(m) = (1)/(n) then (a – d) equals

The sum 20 terms of a series whose rth term is given by T_r=(-1)^r((r^2+r+1)/(r!)) is

The sum of infinite terms of the sequence whose r^("th") term is given by t_(r)=(1)/((r+1)(r+3)) is equal to

If t_(1)=1,t_(r )-t_( r-1)=2^(r-1),r ge 2 , find sum_(r=1)^(n)t_(r ) .