L=lim_(n rarr oo)(n^(3)(e^(1/n)+e^(2/n)+....+e))/((n+1)^(m)(1^(m)+4^(m)+....+n^(2m)))

If L=lim_(nto oo) (n^(3)(e^(1//n)+e^(2//n)+………+e))/((n+1)^(m)(1^(m)+4^(m)+….+n^(2m))) is non zero finite real, then

If L=lim_(nto oo) (n^(3)(e^(1//n)+e^(2//n)+………+e))/((n+1)^(m)(1^(m)+4^(m)+….+n^(2m))) is non zer finite real, then

If L=lim_(nto oo) (n^(3)(e^(1//n)+e^(2//n)+………+e))/((n+1)^(m)(1^(m)+4^(m)+….+n^(2m))) is non zero finite real, then

lim_(n rarr oo)nln( e(1+(1)/(n))^(1-n))

" (e) "lim_(n rarr oo)[(n!)/(n^(n))]^(1/n)

lim_(n rarr oo)(e^(2n)(n!)^(2))/(2n^(2n+1))

Lt_(n rarr oo)(1)/(n)[e^((1)/(n))+e^((2)/(n))+....+e^((n)/(2))]

lim_ (n rarr oo) (e ^ (n)) / ((1+ (1) / (n)) ^ (n ^ (2)))