`lim_(n->oo)(^nP_n)/(^(n+1)P_(n+1)-^nP_n)=`

underset(n to oo)lim (""^(n)P_(n))/(""^(n+1)P_(n+1)-""^(n)P_(n))=

lim_(n to oo)(n!)/((n+1)!-n!)

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

lim_ (n rarr oo) (^ nnP_ (n)) / (^^^ (n + 1) P_ (n + 1) - ^ (n) P_ (n)) =

lim_(n rarr oo)(((n)/(n))^(n)+((n-1)/(n))^(n)+......+((1)/(n))^(n)) equals

The value of lim_(n to oo) [(n!)/(n^(n))]^((1)/(n)) is equal to -

Simplify (nP_4)/((n-1)P_3

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

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0