Limits of series. Hello friends, today it’s all about the limits of series. Have a look!!

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**L’Hôpital’s rule to evaluate the limits of functions**

**Limits of series**

Suppose I have a series where tends to infinity. And my task is to find its limit.

First of all, I’ll look into the highest power of . Next, I’ll divide the whole series with that. So if is the highest power of , then I’ll divide the series with .

Now when tends to infinity, tends to . Then I’ll substitute that value in the series to get its limit.

Now I’ll give some examples of that.

**Examples of the limits of series**

Note: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

**Example 1**

According to Stroud and Booth (2013)* “Find the limiting value of as .”

**Solution**

Now here I have to find out the limiting value of when .

So I can say that I will get the value of

Next, I’ll give it a name, say : Thus it will be

As I can see, here is the highest power of . Hence I’ll divide both the top (numerator) and the bottom (denominator) with . And that gives

When . So Í can say that , . Therefore will be

Next, I’ll simplify it to get

Hence I can conclude that this is the answer to the given example. Now I’ll give another example.

**Example 2**

According to Stroud and Booth (2013)* “Find the limiting value of as .”

**Solution**

Now here I have to find out the limiting value of when .

So I can say that I will get the value of

Next, I’ll give it a name, say : Thus it will be

As I can see, here is the highest power of . Hence I’ll divide both the top (numerator) and the bottom (denominator) with . And that gives

When . So Í can say that , . Therefore will be

Next, I’ll simplify it to get

Hence I can conclude that this is the answer to the given example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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