Question

Find the sum of the series

sum from n=0 to infinity of (-1)^n(8^n)(x^8n)/n!

Answer 1

Maybe I'm missing something, but you need an actual sum? I'm not sure how you would get a value given you have that x term in there. This isn't a radius/interval of convergence problem or anything?

Answer 2

I need the actual sum, yes. I think it's asking to simplify (?) it in terms of cosx or sinx or something like that.

Answer 3

Even if it were a series that represents a known function, without x-values, we just have a function with coefficients determined by n. Unless you mean to say that you think the "sum" isn't a value but a function.

Answer 4

"Find the sum of the series." Is the actual phrasing. And the question is:
\[\sum_{n=0}^{\infty}(-1)^n((8^n)x^(8n))/n!\]

Answer 5

Hmm, interesting
@perl
Any idea how this might actually converge to a sum despite the x term?

Answer 6

I thought I had to manipulate cosx to match it to that, but I can't seem to find a way. :(

Answer 7

i take that back

Answer 8

is that
sum from n=0 to infinity of (-1)^n(8^n)(x^[8n])/n!

Answer 9

or

Answer 10

sum from n=0 to infinity of (-1)^n(8^n)(x^[8^n])/n!

Answer 11

there is a difference

Answer 12

The latter, but it's x^(8n) ! I'm sorry about that.

Answer 13

Oh no, it won't be the latter. Haha, sorry.

Answer 14

ok that can be summed

Answer 15

If it's not a hassle, can I ask how you got that?

Answer 16

exp ( -8 x^8)

Answer 17

why would it be a hassle ? :)

Answer 18

its just time consuming :D

Answer 19

These take so long :(

Answer 20

lets use the series for e^x

Answer 21

better yet, make it e^u

Answer 22

e^u = 1 + u/1! + u^2/2! + u^3/3! + ...

Answer 23

Okay.

Answer 24

the form of that is

sum u^n / n!

Answer 25

Yes.

Answer 26

ok so we almost have the correct form