L_(n rarr oo)((1^(m)+2^(m)+3^(m)+......+n^(m))/(n^(m+1)))=

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

lim_( equals )(n rarr oo){(1^(m)+2^(m)+3^(m)+...+n^(m))/(n^(m+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_ (n rarr oo) nC_ (r) ((m) / (n)) ^ (r) (1- (m) / (n)) ^ (nr) =

lim_ (x rarr oo) ((1) / (n + m) + (1) / (n + 2m) + ... + (1) / (n + nm))

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))

lim_(x rarr0)((2^(m)+x)^((1)/(m))-(2^(n)+x)^((1)/(n)))/(x) is equal to (1)/(m2^(m))-(1)/(n2^(n)) (b) (1)/(m2^(m))+(1)/(n2^(n))(1)/(m2^(-m))-(1)/(n2^(-n))( d) (1)/(m2^(-m))+(1)/(n2^(-n))

Evaluate sum_(m=1)^(oo)sum_(n=1)^(oo)(m^(2)n)/(3^(m)(n*3^(m)+m*3^(n))) .

Evaluate sum_(m=1)^(oo)sum_(n=1)^(oo)(m^(2)n)/(3^(m)(n*3^(m)+m*3^(n))) .