Evaluate: `lim_(nrarroo)(1^(m)+2^(m)+3^(m)+...+n^(m))/(n^(m+1))(mgt-1)`

lim_(n rarr oo) {(1^(m)+2^(m)+3^(m)+…….+n^(m))/(n^(m+1))} equals

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

lim_( equals )(n rarr oo){(1^(m)+2^(m)+3^(m)+...+n^(m))/(n^(m+1))}

Given that lim_(nrarroo) sum_(r=1)^(n) (log_(e)(n^(2)+r^(2))-2log_(e)n)/n = log_(e)2+pi/2-2 , then evaluate : lim_(nrarroo) (1)/(n^(2m))[(n^(2)+1^(2))^(m)(n^(2)+2^(2))^(m) "......"(2n^(2))^(m)]^(1//n) .

{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1)))=

Evaluate: lim_(nrarroo) [(1)/(n+m)+(1)/(n+2m)+(1)/(n+3m)+...+(1)/(n+nm)]

Evaluate : underset(nrarrinfty)lim((1^m+2^m+...+n^m)/n^(m+1))

Evaluate : lim_(x to 1) (x^(m)-1)/(x^(n)-1)

Find the value of sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p)) And hence,find the value of lim_(n rarr oo)(1)/(3^(n))sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p))