Question

`lim_{n→∞}[1/(n^2 + 1) + 2/(n^2 + 1) + 3/(n^2 + 1) + .... + n/(n^2 + 1)]` = ______ 

विकल्प

• 1

• 2

• `1/2`

• 0

Answer 1

`lim_{n→∞}[1/(n^2 + 1) + 2/(n^2 + 1) + 3/(n^2 + 1) + .... + n/(n^2 + 1)]` = `underline(1/2)`

Explanation:

Given limit = `lim_{n→∞} (1 + 2 + 3 + ... + n)/(1 + n^2)`

= `lim_{n→∞} (sumn)/(1 + n^2)`

= `lim_{n→∞} 1/2 (n(n + 1))/(1 + n^2)`

= `lim_{n→∞} 1/2 ((1 + 1/n))/((1/n^2 + 1))`

= `1/2. 1 = 1/2`