1. ## 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!

2. Hi

$\sum_{k=0}^{\infty} \frac{(-1)^k \:\theta^{2k+1}}{(2k+1)!} = \sin \theta$

You can find this relation starting from

$e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}$ and $\sin x = \frac{e^{ix}-e^{-ix}}{2i}$