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# Proving the limit of a sequence using binomial theorem watch

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.

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