Example 1

Geometric: a=1, r=0.5 → S∞=2 (converges)

Example 2

Geometric: a=3, r=2 (diverges)

Example 3

p-Series: p=2 (Basel, π²/6 ≈ 1.645)

Example 4

p-Series: p=0.5 (diverges)

Example 5

Harmonic series: Σ 1/n (always diverges)