[SOLVED] Finding the limit of a sequence.

**ilikedmath** · November 15th 2008, 06:08 AM

I need to find the limit of {(1 + $\frac{1}{2n})^n$ }, and justify my answer.

I know that $\stackrel{\lim}{n\rightarrow\infty}$ (1 + $\frac{1}{n})^n$ = e.

Can I use $\frac{n}{2}$ for my 'n,' so I get:

$\stackrel{\lim}{n\rightarrow\infty}$ (1 + $\frac{1}{2(\frac{n}{2})})^\frac{n}{2}$

= $\stackrel{\lim}{n\rightarrow\infty}$ (1 + $\frac{1}{n})^\frac{n}{2}$

= $\stackrel{\lim}{n\rightarrow\infty}$ $[(1 + \frac{1}{n})^n]^\frac{1}{2}$

= $\stackrel{\lim}{n\rightarrow\infty}$ $e^\frac{1}{2}$ = $\sqrt{e}$

Or is $\frac{n}{2}$ not a legitimate choice since I am dealing with naturals?

Thanks for your time,
ilikedmath

**Plato** · November 15th 2008, 06:13 AM

That is the correct answer.
You might have seen this $\left( {1 + \frac{1} {{2n}}} \right)^n = \left( {1 + \frac{{1/2}} {n}} \right)^n \to e^{\frac{1} {2}}$

**ilikedmath** · November 15th 2008, 06:28 AM

Originally Posted by Plato

That is the correct answer.
You might have seen this $\left( {1 + \frac{1} {{2n}}} \right)^n = \left( {1 + \frac{{1/2}} {n}} \right)^n \to e^{\frac{1} {2}}$

Thanks, Plato! You're such a lifesaver!

It seems we're getting some spam posts on some threads here. I've noticed they're all 'newbies' too with a very few number of posts. How can we delete those spam posts?

**Krizalid** · November 15th 2008, 06:32 AM

Originally Posted by ilikedmath

It seems we're getting some spam posts on some threads here. I've noticed they're all 'newbies' too with a very few number of posts. How can we delete those spam posts?

Don't worry, Moderators will take care of that.

Meanwhile, if you see more spamming posts, report them.

**ilikedmath** · November 15th 2008, 06:35 AM

Originally Posted by Krizalid

Don't worry, Moderators will take care of that.

Meanwhile, if you see more spamming posts, report them.

All right, thanks. I just found the report button. I'll report those immediately!

**Krizalid** · November 15th 2008, 06:38 AM

This one,

Thread: [SOLVED] Finding the limit of a sequence.

LinkBack

Thread Tools

Display

[SOLVED] Finding the limit of a sequence.

Similar Math Help Forum Discussions

sequence converge, finding its limit.

[SOLVED] Limit of a sequence - recursion

determine if a sequence converges/finding the limit

[SOLVED] Calculating limit of a sequence

finding the limit of the sequence

Search Tags