If ` ∑_ (i = 1)^T T y = ( n^ 2 + 3 n )^ 2 + 2 ⋅ ( n^ 2 + 3 n )` , then `∑_ (k =1)^oo 1/ (Tn)` is

If Delta_(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " then " sum_(k=1)^(n) Delta_(k) is equal to

If sum_(r=1)^(n)t_(r)=(1)/(4)n(n+1)(n+2)(n+3) then value of (1)/(sum_(r=1)^(oo)((1)/(t_(r)))) is

If S_(n)=sum_(r=1)^(n)t_(r)=(1)/(6)n(2n^(2)+9n+13), then sum_(r=1)^(oo)(1)/(r*sqrt(t)) equals

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) then 4(lim_(x rarr oo)sum_(x-1)^(n)(1)/(T_(r))) is equal to

If T_n = 3n +8 , then T_(n-1) = ________.

If sum _( r -1) ^(n) T_(r) = (n (n +1)(n+2))/(3), then lim _(x to oo) sum _(r =1) ^(n) (2008)/(T_(r))=

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