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

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{:(" "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))}

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

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

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

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lim_ (n rarr oo) nC_ (r) ((m) / (n)) ^ (r) (1- (m) / (n)) ^ (nr) =

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If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)(2^n-1)^m