Hey can you please solve 6 and 7 please :)

I ll definitely vote :)

6. Let a be a real number. Consider the series a 00 an, TO where an= cos(n) 2n +1 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. Answers without reasoning will be given 0. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally, NP 7. Read about the Integral Test in Section 11.3 and, specifically, through example 2 to see how the Integral Test can be applied to determine the convergence of the p-series Then, carefully apply the Integral Test to determine all values of p for which the series In(n) NP is convergent. As part of your solution, you should convince us that all the conditions of the Integral Test are met