If `t_(r)=(1^(2)+2^(2)+3^(2)+….+r^(2))/(1^(3)+2^(3)+3^(3)+…+r^(3)), S_(n)=sum_(r=1)^(n)(-1)^(r)t_(r)`, then `lim_(nrarroo)((1)/(3-S_(n)))=`

If t=(1^(2)+2^(2)+3^(2)+...r^(2))/(1^(3)+2^(3)+3^(3)+....+r^(3)), S_(n) = overset(n) underset(r=1) sum(-1)^(r)t_(r) then lim_(n to oo) ((1)/(3)-S_(n))=

S_(n)=sum_(r=1)^(n)(r)/(1.3.5.7......(2r+1)) then

Find sum_(r=1)^(n)(1^(2)+2^(2)+3^(3)+...+r^(2))/(r+1)

If S_(1)= sum_(r=1)^(n) r , S_(2) = sum_(r=1)^(n) r^(2),S_(3) = sum_(r=1)^(n)r^(3) then : lim_(n to oo ) (S_(1)(1+(S_(8))/8))/((S_(2))^(2)) =

If S_(n) = sum_(r=1)^(n) (r )/(1.3.5.7"……"(2r+1)) , then

If Delta_(r)=|(r-1,n,6),((r-1)^(2),2n^(2),4n-2),((r-1)^(3),3n^(3),3n^(2)-3n)| then sum_(r=1)^(n)Delta_(r)=

sum_(r=1)^(n)r^(3)=f(n) then sum_(r=1)^(n)(2r-1)^(3) is equal to

If sum_(r=1)^(n)T_(r)=(3^(n)-1), then find the sum of sum_(r=1)^(n)(1)/(T_(r))

If sum_(r=1)^(n) T_(r)=(n(n+1)(n+2)(n+3))/(8) , then lim_(ntooo) sum_(r=1)^(n) (1)/(T_(r))=