I've tried plugging the series in Wolfram to first of all check if it converges but it doesn't return anything useful. Moreover, just computing $\Phi(-100)$ returns something useless. Looking at the distribution function of the standard normal distribution it is obvious that $\Phi(-100) \approx 0$, but I guess the same can be said about $1/100$, while the infinite series of $1/n$ is infinity.
Is this series even defined, i.e. can it be computed, or are some problems that don't allow computation?