Yes, Consider Un = (-1)^n*n = -1, 2, -3, 4, ...
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Diverge!
When you take the integral using the series as integrand, it converges if the integral worked out to be a number. If it's infinte, the series diverge.
The noun forms for the verb to diverge are divergence and the gerund, diverging.
Diverge means move away from each other and go in different directions. Synonyms of the word diverge are split, separate, branch off, and bifurcate.
6; alternating decreasing series, by twos