`lim_(x rarr oo) (1+2+3+...+n)/(1^(2)+2^(2)+3^(2)+...+n^(2))` किसके बराबर है ?

Options

A. 5
B. 2
C. 1
D. 0

Answer

D

Explanation

`underset(nrarroo)lim(1+2+3+...+n)/(1^(2)+2^(2)+3^(2)+...+n^(2))`
`=underset(nrarroo)lim((n(2+1))/(2))/((n(n+1)(2n+1))/(6))`
`=underset(nrarroo)lim(n(n+1))/(2)xx(6)/(n(n+1)(2n+1))`
`=underset(nrarroo)lim(3)/(2n+1)=0`