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f) The series ∑j=1∞(–1)j sin j / j3 converges by the comparison test, because |(–1)j sin j / j3| ≤ 1/ j3 and the series ∑j=1∞ 1/ jp converges for any p > 1. Here p = 3.
g) The series ∑n=2∞ 1/n(ln n)2 converges since the integral ∫2∞ 1/x(ln x)2 dx = – 1/ln x ]2∞ = 1/ln 2 converges (note that limx→+∞1/ln x = 0).
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