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

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

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

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

The r th term of a series is given by t_r=r/(1+r^2+r^4) , then lim(n->oo)sum_(r=1)^n(t_r)

If sum of x terms of a series is S_(x)=(1)/((2x+3)(2x+1)) whose r^(th) term is T_(r) . Then, sum_(r=1)^(n) (1)/(T_(r)) is equal to

A series whose n^(th) term is (n/x) , then sum of r terms will be

Write down the series whose r^(th) term is 3. 2 ^(r + 1 ) . Is it a geometric series ?

Prove that the sum of n terms of the reciprocals of the terms of the series a, ar, ar^(2),…" is "(1-r^(n))/(a(1-r)r^(n-1))

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_3+..+S_n= (A) (na)/(1-r)-(ar(1-r^n))/((1-r)^2 (B) (na)/(1-r)-(ar(1+r^n))/((1+r)^2 (C) (na)/(1-r)-(a(1-r^n))/((1-r)^2 (D) none of these