Question: Problem 2. Let fbe a function defined on[1,).InHW3, Problem 8, you proved the integral test forconvergence: Iffis positive-valued and decreasing, the seriesn=1f(n)converges if and only

Problem 2. Let fbe a function defined on[1,).InHW3, Problem 8, you proved the integral test forconvergence: Iffis positive-valued and decreasing, the seriesn=1f(n)converges if and only if the limitlimN1Nfexists.(a) Show by example that the conclusion may fail iffis not assumed tobe positive-valued.(b) Show by example that the conclusion may fail ifffis not integrable. Your example should be a function for which theintegrals 1Nf still exist.

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