How do you test this series for convergence or divergence? 4/7 - 4/8 + 4/9 - 4/10 + 4/11 - ...

... ?

The function is neither an arithmetic nor geometric progression so we can check its convergence by checking the value of each of the given terms.

If we evaluate the fractions, or just observe that the denominator is increasing, we can see that the absolute value of the series will decrease. Therefore, it will converge.