[lim_(n rarr oo)(1^(p)+2^(p)+3^(p)+....+n^(p))/(n^(p+1))=],[[" (a) "(1)/(p+1)," (b) "(1)/(1-p)],[" (c) "(1)/(p)-(1)/(p-1)," (d) "(1)/(P+2)]]

The value of lim_(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1)) is -

Evaluate: lim_(n rarr oo)(n^(p)sin^(2)(n!))/(n+1)

lim_(n rarr0){(p^((1)/(n))+q^((1)/(n)))/(2)}^(n),p,q>0

If P=lim_(n rarr oo)(ea^(2)*e^(3)a^(4)...e^(n-1)a^(n))^((1)/(n^(2)+1)) then P^(4) equals

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

If 0ltpltq then lim_ (n rarr oo)(q^(n)+p^(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

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

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