(2 points) We will determine whether the series 00 H N n=2 n(In n) 1/4 is convergent or divergent using the integral test. First we must show that...

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(2 points) We will determine whether the series00HNn=2n(In n) 1/4is convergent or divergent using the integral test. First we must show that the related functionf(x) = -x(In .x) 1/4is continuous, positive, and decreasing on the interval [2, co).It should be clear that f(x) is continuous and positive on [2, co). To see that f (x) is decreasing on [2, co ), compute thederivative of f .= (x) , fSince f' (x) is negative on [2, co ) (verify this!), we conclude that f is decreasing on [2, co).Now by the Integral Test, the series