\(a_{n} = \frac{n}{\sqrt{5 + n}}\)

convergent?

This answer is restricted. Please login to view the answer of this question.

Login NowA sequence is an ordered list of things. Such thinks may finite or infinite. In a sequence, the terms are separated by commas(,).

**Definition:**

A sequence is a list of numbers which are written as a definite order:

a_{1}, a_{2}, a_{3}, a_{4}, …….. a_{n}

Here, a_{1} is first term, a_{2} is second term and likewise a_{n} is the n^{th} term of the series.

For example:

{1, 2, 3, 4, 5 ……} is a sequence

**Problem Part:**

The general form of the series is

\(a_{n} = \frac{n}{\sqrt{5 + n}}\)

Using D’Alembert’s Ratio Test,

\(\lim_{n \to ∞} a_n = \lim_{n \to ∞} \frac{n}{\sqrt{5 + n}}\)

\(= \lim_{n \to ∞} \frac{1}{ \frac{1}{n} \sqrt{5 + n}}\)

\(= \lim_{n \to ∞} \frac{1}{ \sqrt{\frac{5}{n^2} + \frac{1}{n}}}\)

\(= \lim_{n \to ∞} \frac{1}{ \sqrt{\frac{5}{∞} + \frac{1}{∞}}}\)

\(= \frac{1}{∞}\)

= 0

So, The given sequence is convergent

If you found any type of error on the answer then please mention on the comment or report an answer or submit your new answer.

Click here to submit your answer.

HAMROCSIT.COM

## Discussion