Sum of infinite series pls

Question

I've looked at a lot of examples of infinite series, but I still don't get how to do this one.

$$-490\sum_{n=3}^∞ \left(\frac{-3}{7}\right)^n$$

Answer 1

Well, no, you have not looked at a lot of examples, if you don't know one of the most famous ones: The Geometric series. I would suggest to look it up and then find out why you can apply it here. Hint: $|-3/7|<1$.

Answer 2

Hint:

use the geometric series with $|x|<1$ $${\displaystyle {\begin{aligned}{\frac {1}{1-x}}&=\sum _{n=0}^{\infty }x^{n}\\\end{aligned}}}=1+x+x^2+\sum _{n=3}^{\infty }x^{n}$$