Please show all work, step by step. Thank you so much!

7'. (10 pts) Show that the function determined by the terms of the given series satises the hypotheses of the Integral Test= and then use the Integral Test to determine whether the series sum converges or diverges. 1 kZl (a) Make a plot of: f(X) = x211 {b} Is f(x} always positive and decreasing from 1 {1: X {I +inf ? {yes or no} (c) Perform the integral test. Does the series converge. diverge. or inconclusive? {(1} Perform the p-test. Does the series converge, diverge, or inclusive. (e) If your answers to (c) and ({1} are difference, how do you resolve the difference