` lim _( x to oo) ( 1+ 2+ 3 + . . . . . + x )/(x^(2))` का मान ज्ञात कीजिये ।

Options

A. `0`
B. `1/2`
C. `1`
D. `3/2`

Answer

B

Explanation

` ( x to oo) ( 1+ 2 + 3 + . . . . . + x)/(x^(2))= lim _( x to oo) (x(x+1))/( 2x^(2))`
` = lim _( x to oo) (x^(2) (1+ 1/x))/(2x^(2))`
` = lim _ ( x to oo) (1+1/x)/2`
` 1/2 " "[ :' lim_( x to oo) 1/x = 0 ]`
अतः अभीष्ट मान = `1/2`