Find the true value using exponential series

[Denton91]

Hello

I've been given a problem of finding the true value of 2e^0.5 to 2 d.P using exponential series. From what I've learnt, the exponential series is:
'e^x=1+x+x^n/n!'.

I've used this for all the examples I've done and its always worked, but this is the first time I've had a number in front of e. Because of the 2, i changed the first term to 2, but still couldn't find.the answer (I know the answer should be 3.29).

I could post a picture of my workings, but I've been told off on a previous forum for my file size being too big

Also, if you need more information of what I've done, just ask, I'm having to post from my phone and it's.proving difficult, hense the lack of detail

 

[HallsofIvy]

Hello

I've been given a problem of finding the true value of 2e^0.5 to 2 d.P using exponential series. From what I've learnt, the exponential series is:
'e^x=1+x+x^n/n!'.

Well, you are missing a lot! It is 'e^x= 1+ x+ x^2/2+ x^3/3!+ ...+ x^n/n!+ ...'
I presume that is what you meant.

I've used this for all the examples I've done and its always worked, but this is the first time I've had a number in front of e. Because of the 2, i changed the first term to 2, but still couldn't find.the answer (I know the answer should be 3.29).

You know the 2 just means "multiply by two" don't you? So you could just use the previous formula and then multiply by 2. But if you want the "2" in the formula itself, you need to multiply every term by two:
2e^x= 2(1+ x+ x^2/2+ x^3/3!+ ...+ x^n/n!+ ...)= 2+ 2x+ x^2+ 2(x^3/3!)+ ...+ 2(x^n/n!)+ ...

I could post a picture of my workings, but I've been told off on a previous forum for my file size being too big

Also, if you need more information of what I've done, just ask, I'm having to post from my phone and it's.proving difficult, hense the lack of detail

 

[Denton91]

Yes, I did know that I missed all the other formula out, its just that typing on my phone was working to be really slow. So I apologise if I led to confusion.

Also, I do know that the 2 means to multiply by 2, but when I attempted the multiplying my original findings with 2 I was only getting to 3.14. However, I've tried that many ways that I may have confused myself on the way.

Thanks for your help, I will start a fresh and try again.

 

[Denton91]

Thank you that has worked. I think I need to learn to take a step back and go back to it.

Also, am I right in thinking that because it is to 2 d.p, then you stop once you have got the same 2 d.p's 2 or 3 times in a row...otherwise you will be going on forever

 

[stapel]

Thank you that has worked. I think I need to learn to take a step back and go back to it.

Also, am I right in thinking that because it is to 2 d.p, then you stop once you have got the same 2 d.p's 2 or 3 times in a row...otherwise you will be going on forever

Once the terms you're adding (from the summation formula) are small enough that they won't ever change the decimal places that you "care" about, yes, you can stop. Good thinking!