Paul M. answered • 04/04/19

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D_{n} = 3 + 4n for n≥0

N_{n} = 7 + 4n for n≥0

a_{n} = (4n + 7)/(4n + 3) = [4 + (7/n)]/[4 + (3/n)] for n>0

thus lim as n->∞ a_{n} = 1 and therefore, the series cannot converge.

In order for an infinite series (sum) to converge the sequence which forms the series must converge to 0.