underset n rarr oo Lt{(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))......(1+(n^(2))/(n^(2)))}^(1/n)=

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))

lim_(n rarr oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))+...+(n)/(n^(2)))

lim_(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is :

Lt_(x to oo)[(1)/(n^(2)-1)+(2)/(n^(2)-1)+....+(n)/(n^(2)-1)]=

Lt_(n rarr oo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/(n^(2)))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2))).....(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))]

lim_ (n rarr oo) [(1+ (1) / (n ^ (2)))) (1+ (2 ^ (2)) / (n ^ (2))) (1+ (3 ^ (2) ) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2)))] ^ ((1) / (n))

{:(" "Lt),(n rarr oo):} [(1)/(1-n^(2))+(2)/(1-n^(2))+...+(n)/(1-n^(2))]=

Lim {x rarr oo} {(1+ (1) / (n ^ (2))) ^ ((2) / (n ^ (2))) (1+ (4) / (n ^ (2)) ) ^ ((4) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2))) ^ (2 (n) / (n ^ (2)))}