Let `T_n` be the `n^(th)` term of a sequence for `n=1,2,3,4....if 4T_(n+1)=T_n and T_5=1/(2560)` then the value of `sum_(n=1)^oo(T_n*T_(n+1))` is equal to

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2))/(6), then the value of sum_(r=1)^(oo)((1)/(T_(r))) is equal to

Let t_(n)=n.(n!) Then sum_(n=1)^(15)t_(n) is equal to

Let t_n =n.(n!) Then sum_(n=1)^(15) t_n is equal to

If n^(th) term (T_(n)) of the sequece is given by the relation T_(n+1)=T_(n)+2^(n),(n epsilonN) and T_(1)=3 , then the value of sum_(r=1)^(oo)1/(T_(r)-1) equals

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……

The fifth term of the sequence for which t_1= 1, t_2 = 2 and t_(n + 2) = t_n + t_(n + 1) is

Find the first five terms of the sequence for which t_(1)=1,t_(2)=2 and t_(n+2)=t_(n)+t+(n+1)

Let r^(th) term t _(r) of a series if given by t _(c ) = (r )/(1+r^(2) + r^(4)) . Then lim _(n to oo) sum _(r =1) ^(n) t _(r) is equal to :