Assertion-reason On Convergence

This assertion-reason problem hinges on the distinction between a necessary and a sufficient condition for convergence, a subtlety JEE Advanced probes carefully. The assertion is true: the harmonic series Σ1/n is the classic divergent series, shown by grouping terms into blocks each exceeding 1/2. The reason is false: terms tending to zero is necessary but not sufficient for convergence, and the harmonic series itself is the counterexample, since its terms vanish yet the sum is infinite. Because a true assertion accompanies a false reason, the correct choice is that the assertion is true and the reason is false. The option claiming both true and explanatory is wrong since the reason is false. The option marking the assertion false contradicts harmonic divergence. The both-true-non-explanatory option also fails because the reason is simply untrue. The deeper point is that the vanishing-term condition is only the contrapositive of a divergence test: if terms do not approach zero the series must diverge, but the converse fails, and the harmonic series is the canonical demonstration that convergence demands a faster decay. Plausibility check: the harmonic partial sums grow like the natural logarithm of n, which increases without bound, confirming divergence despite shrinking terms.