# Estimate value of e

• Oct 27th 2012, 04:35 PM
Eraser147
Estimate value of e
Attachment 25428 Click image to enlarge please.
• Oct 27th 2012, 04:38 PM
skeeter
Re: Estimate value of e
the expression posted is very good approximation of e3
• Oct 27th 2012, 06:18 PM
Eraser147
Re: Estimate value of e
Can you show me the steps please?
• Oct 27th 2012, 06:34 PM
Plato
Re: Estimate value of e
Quote:

Originally Posted by Eraser147
Can you show me the steps please?

It is well known that $\lim _{n \to \infty } \left( {1 + \frac{r}{n}} \right)^n \to e^r$.

So if $n=10^{100}$ then from the limit we see it is an approximation for $e^3$
• Oct 27th 2012, 06:42 PM
Eraser147
Re: Estimate value of e
I don't know limits yet. Is there another explanation?
• Oct 27th 2012, 06:55 PM
Plato
Re: Estimate value of e
Quote:

Originally Posted by Eraser147
I don't know limits yet. Is there another explanation?

Absolutely none that I know.
If you don't know about limits, then I cannot understand why you were asked this question. What does question relate to? Is it in any particular course?
• Oct 27th 2012, 07:01 PM
Eraser147
Re: Estimate value of e
it's related to natural logs. That's all I learned in class.
• Oct 30th 2012, 10:18 PM
Salahuddin559
Re: Estimate value of e
One sec, there is always a simple explanation. First consider this.

(1 + 1/1)^1 = 1.
(1 + 1/2)^2 = 9/4 = 2.25.
(1 + 1/3)^3 = 64/27 = 2.37
(1 + 1/4)^4 = 625/256 = 2.44

as you can see, the values are approaching something, right. For higher values of n, the expression (1 + 1/n)^n likely, remains constant with little variation. Similarly, use a calculator or some math programs and work out what he is saying, you will see the point.

Salahuddin
Maths online