
exponential?
ive been sent this problem and am a little stuck:
r = 1  sum_(k=0)^infinity((1)^k theta^(1+2k))/(1+2k)!
there was no multiplier put between the k and the theta, i'm guessing this was just a typo? so it would look like this:
r = 1  sum_(k=0)^infinity((1)^k*theta^(1+2k))/(1+2k)!
the sum_(k=0)^infinity(theta^(1+2k))/(1+2k)! looks like an exponential. is this right, even though the term is 1+2k? could it then be written as:
r = 1  e^theta*(1)^k ??
three variables now, i'm confused. my math is very rusty.
any help or guidance would be great
thank!

Hi
$\displaystyle \sum_{k=0}^{\infty} \frac{(1)^k \:\theta^{2k+1}}{(2k+1)!} = \sin \theta$
You can find this relation starting from
$\displaystyle e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}$ and $\displaystyle \sin x = \frac{e^{ix}e^{ix}}{2i}$