You are Here: Home >< Maths

# Proving the limit of a sequence using binomial theorem

Announcements Posted on
Why bother with a post grad course - waste of time? 17-10-2016
1. Here's the question:

I worked out the limit to be 3/2. I confirmed this using wolphram alpha.
However when I try to use binomial theorem to prove this, I can't seem to get the same answer. My workings so far are:
Attachment 559898559900

where am I going wrong?

Thanks, Charlie.
Attached Images

2. (Original post by TurboCarlos1)

where am I going wrong?

Thanks, Charlie.
Nope, nope, nope. You can't apply limits randomly like that. Not if they don't exist.

since doesn't exist.

so the limiting value is since all other terms are of the order at most and go to 0 in the limit.
3. (Original post by TurboCarlos1)
Here's the question:

I worked out the limit to be 3/2. I confirmed this using wolphram alpha.
However when I try to use binomial theorem to prove this, I can't seem to get the same answer. My workings so far are:
Attachment 559898559900

where am I going wrong?

Thanks, Charlie.
You're subbing in limits too hastily. Always be careful with stuff like this. You note that when the 1 + 3/2n + blah is multiplied by the n, you get n + 3/2 + (a load of stuff that tends to 0) giving you overall n + 3/2 + (a load of stuff that tends to 0) - n = 3/2 + (a load of stuff that tends to 0), which clearly tends to 3/2
4. thanks to you both, got it.
5. (Original post by TurboCarlos1)
thanks to you both, got it.
No worries.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: July 8, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### A level maths

Which modules should I take?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams