Is the series (-1)^n * (sin^2(n)/n) convergent or divergent using ratio, root, or integral test?

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Is the series (-1)^n * (sin^2(n)/n) convergent or divergent using ratio, root, or integral test?

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you can compare this series to the alternating harmonic series: Sum[ (-1)^n/n] which converges each term in your series is less than or equal to each term in the alternating harmonic series, since the value of sin(n) must always be equal to or less than one therefore, if each term in a series is less than or equal to a series that converges, the series in question converges this assumes that you have established in class that the alternating harmonic series has converged; look this up in your book or search for it on line hope this helps

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