Determine a function which is represented by that summation given below

Question

anonymous · Answer

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

anonymous · Answer

what this?

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

or do we account for the factorials also i spose

anonymous · Answer

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

anonymous · Answer

you got it, backward taylor series

anonymous · Answer

You don't need to do that amister.

amistre64 · Answer

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

anonymous · Answer

Haha. ok.

anonymous · Answer

what factorial

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

Trial & error might help

anonymous · Answer

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