### Sage seems to be improperly computing an infinite sum

Reference this question: https://ask.sagemath.org/question/35305/how-i-can-test-this-equality-with-sage/

Here is the evaluation of an infinite sum in sage:

```
var('n')
f(n) = (-1)^(n+1)/(3*n+6*(-1)^n)
sum(f(2*n)+f(2*n+1),n,0,oo)
1/3*log(2) - 7/9
```

Evaluating the same sum in Mathematica:

```
f[n_] := (-1)^(n + 1)/(3*n + 6*(-1)^n)
Sum[f[2*n] + f[2*n + 1], {n, 0, Infinity}]
1/6 (-2 + Log[4])
```

Sage seems to be giving an incorrect solution. Am I missing something?