First slide

Introduction to limits

Question

If $S_{n} = \sum_{k = 1}^{n} a_{k} and lim_{n \to \infty} a_{n} = a$ , then $lim_{n \to \infty} \frac{S_{n + 1} - S_{n}}{\sqrt{\sum_{k = 1}^{n} k}}$ is equal to

Moderate

A

0
B

$a$
C

$\sqrt{2} a$
D

$2 a$

Solution

We have,
$lim_{n \to \infty} \frac{S_{n + 1} - S_{n}}{\sqrt{\sum_{k = 1}^{n} k}} = lim_{n \to \infty} \frac{a_{n + 1}}{\sqrt{\frac{n (n + 1)}{2}}} = 0$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App