_ x 1+2+3+ +n 1+3+5+ +(2 n-1) = - Vidyadip

MCQ

$\lim _{x \rightarrow \infty} \frac{1+2+3+\ldots+n}{1+3+5+\ldots+(2 n-1)}=$

A
1
B
$\frac{3}{2}$
✓
$\frac{1}{2}$
D
2

✓

Answer

Correct option: C.

$\frac{1}{2}$

(C)
$\lim _{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{1+3+5+\ldots+(2 n-1)}=\lim _{n \rightarrow \infty} \frac{\frac{n(n+1)}{2}}{n^2}$
$=\lim _{n \rightarrow \infty} \frac{n(n+1)}{2 n^2}$
$=\lim _{n \rightarrow \infty} \frac{n^2+n}{2 n^2}=\frac{1}{2}$

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