The given series can be written as: . The sine function can be expressed as a power series as .
If you let , you get that your series (with the pulled out) is just , so your series converges to .
You should know how to write a given series using notation and then how to manipulate the starting index of that series as needed to make the series look like the power series expansion of some popular function. Remembering the power series expansion for popular functions (trig, exponential, logs, etc.) helps so you know what you are aiming for. Also remember you can move constants into and out of a series as you please. I don't know what else to say. What's the problem you're having trouble with?