`underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n)` is

The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(sqrt(n))/(sqrt(r ) (3 sqrt(r)+4)sqrt(n)^(2)) is equal to

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to

Use Sandwich theorem to evaluate : underset( n rarr oo) ( "Lim") underset(k=n^(2))overset((n+1)^(2))sum (1)/( sqrt( k ))

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

If k=underset(r=0)overset(n)(sum)(1)/(.^(n)C_(r)) , then underset(r=0)overset(n)(sum)(r)/(.^(n)C_(r)) is equal to

The limit of the series underset(r=1)overset(n)sum (r)/(1+r^(2)+r^(4)) as n approaches infinity, is

lim_(n to oo) sum_(r=1)^(n) (1)/(n)e^(r//n) is