# Thread: Estimate value of e

1. ## Estimate value of e

Click image to enlarge please.

2. ## Re: Estimate value of e

the expression posted is very good approximation of e3

3. ## Re: Estimate value of e

Can you show me the steps please?

4. ## Re: Estimate value of e

Originally Posted by Eraser147
Can you show me the steps please?
It is well known that $\displaystyle \lim _{n \to \infty } \left( {1 + \frac{r}{n}} \right)^n \to e^r$.

So if $\displaystyle n=10^{100}$ then from the limit we see it is an approximation for $\displaystyle e^3$

5. ## Re: Estimate value of e

I don't know limits yet. Is there another explanation?

6. ## Re: Estimate value of e

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?

7. ## Re: Estimate value of e

it's related to natural logs. That's all I learned in class.

8. ## 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