An infinite series with terms tending to zero may still diverge - the harmonic series does. Why is "the terms shrink to zero" not enough for convergence?

C. Because what matters is how fast the terms shrink, not that they do.

The grouping argument makes it concrete: 1/3 + 1/4 > 1/2, the next four terms also exceed 1/2, and so on indefinitely. Terms going to zero is necessary and not sufficient, and the p-series boundary is sharp at p = 1. The computing consequence is that partial sums are not evidence, the harmonic series passes 20 only after about 250 million terms.