Question

Hello. Can I start my iteration when n=-1, no? Let's take for an example this series of expansion: 1/x +1 + x/2! +x^2/3! + ... + x^n/n! Can I say "the algebraic sum from n=-1 to n=infinity"?

Answer 1

I am asking this because my instructor marked my answer wrong and he won't talk to me.

Answer 2

No, the index n can only be positive. And what does (-1)! mean?

Answer 3

that's why i put (n+1)! haha

Answer 4

Ahhhhhh...gotcha. I like the idea. But you have to have positive indices.

Answer 5

so should I have just removed my lnx from my series representation?

Answer 6

No, the teacher was correct. You must write it as an intergral, or a sum using sigma.

Answer 7

the question is evaluate the integral of e^-x (1/x)dx

Answer 8

Exactly, you have to leave it as an intergral equal to a sum.

Answer 9

Can I do that? Oh. I never know. XD

Answer 10

but can I use lnx + series representation, too?

Answer 11

Should equal the sum:
\[\sum_{n=0}^{\infty}\frac{x^n}{(n!)x}=\sum_{n=0}^{\infty}\frac{x^{n-1}}{n!} \]
Which is easy to integrate.

Answer 12

You can bring the x in the sum because its being summed over n, not x.

Answer 13

And since you're integrating with respect to x the n! is a "constant" of sorts and can be neglected (there is no antiderivative for n!).

Answer 14

Or am I inventing math?

Answer 15

http://www.wolframalpha.com/input/?i=integral+of+e^(-x)%2Fx
Seems plausible.

Answer 16

(-x)^n / n*n! is this it?

Answer 17

+C???????

Answer 18

\[\sum_{n=1}^{\infty}\frac{(-x)^{n}}{x(n!)}\]
You can't bring n's in arbitrarily because its summed over n.

Answer 19

I got the integral of that (-x)^n ln x / n!

Answer 20

but whenever i iterate it, all terms contain "lnx" -.-

Answer 21

Ohhhhh I see what you mean. I don't know how to help that man.

Answer 22

Oh thanks. my question is answered anyway. :D thanks!