Question

2. if the sum from n=1 to infinity of a(sub n) converges and a(sub n) does not =0, then the sun from n=1 to infinity of 1/(a(sub n)) diverges.
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Answer 1

If the original series converges, a(n) gets vanishingly small for large n
That means 1/a(n) gets huge for large n, approaching 1/0