## anonymous 5 years ago Determine a function which is represented by that summation given below

1. anonymous

$\sum _{n=1}^{\infty } \text{nx}^n$

2. anonymous

what this?

3. amistre64

x + 2x^2 + 3x^3 + 4x^4 + ... + nx^(n)+.... like that?

4. anonymous

no,you know how f(x)=e^x is represented by $1+x+x^2/2!+.....$ so this is reverse where you are trying to figure out function based on series given

5. amistre64

or do we want this to be a backwards taylor series?

6. amistre64

y = ? y' = 1 y''=2 y'''=3 y'''' = 4 then right?

7. amistre64

or do we account for the factorials also i spose

8. anonymous

This can be written as a geometric series. Use that to find the function that represents the summation.

9. anonymous

you got it, backward taylor series

10. anonymous

You don't need to do that amister.

11. amistre64

lol.... i do if I wanna understand whats going on ;)

12. anonymous

Haha. ok.

13. anonymous

what factorial

14. amistre64

taylor has factorials under them; i just assume they are a part of it

15. anonymous

no, it is the series, I think we want the function that it represent

16. amistre64

1 1 2 6 120 720 5040 40320 362880 3628800 those things

17. amistre64

i got more reading to do about series to be able to understand them better :)

18. anonymous

So Taylor polynomial of a function is this. We want the function?

19. anonymous

Trial & error might help

20. anonymous

$\sum_{n=1}^{Infinity}nx^n$ = x+2x^2+3x^3+.....+nx^n