### How I can test this equality with sage?

How I can test this equality?

$$\sum_{n=0}^\infty\frac{(-1)^{n+1}}{3 n+6 (-1)^n}=\frac{\log(2)-1}{3}$$

Im interested in symbolic tests and numerical tests. My knowledge about the way to do this with sage (in general in any CAS, not only sage) is near to zero. Any help, link, etc. will be appreciated, thank you.

**EDIT:** I tried to use this code ~~(with ~~(what is a slight ~~simplification)~~simplification of the above equality)

```
var("n")
sum(1/(n*(-1)^n+2),n,0,oo) == -log(2)+1
```

but, as expected, it dont work.