van=facebook.com/LearningCalculus$

assume(k>1);

limit(n^(k-1)/n^k,n,inf);

limit((n-1)^(k-1)/n^k,n,inf);

(1+sum(i^(k-1),i,2,n))/n^k;

s:1/n^k + sum(i^(k-1)/n^k,i,2,inf);

limit(%,n,inf);

t:(1/n)*sum((i/n)^k,i,1,n);

s=t;

is(equal(s,t));