If `u(n)=prod_(r=0)^n(1+r^2/n^2)^r "then" lim_(nrarroo) (u)^((-4)/n^2`

If f(n)=prod_(r=1)^(n)cos r,n in N , then

Consider the sequence u_(n)=sum_(r=1)^(n)(r)/(2^(r)),n>=1 then the lim it_(n rarr oo)u_(n)

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 U_(n)=(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))^(2).............(1+(n^(2))/(n^(2)))^(n) m then lim_(n to oo)(U_(n))^((-4)/(n^(2))) is equal to

If sum_(r=1)^(n)a_(r)=(1)/(6)n(n+1)(n+2) for all n>=1 then lim_(n rarr oo)sum_(r=1)^(n)(1)/(a_(r)) is

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 A_(r)=[((1)/(r(r+1)),(1)/(3^(r ))),(2,3)] , then lim_(nrarroo)Sigma_(r=1)^(n)|A_(r)| is equal to

If f(x) is integrable over [1,], then int_(2)^(2)f(x)dx is equal to lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=n+1)^(2n)f((r)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)f((r+n)/(n))lim_(n rarr oo)(1)/(n)sum_(r=1)^(2n)f((r)/(n))