00 n 7' Prologue: The series 2 converges when ~1 1. This is true regardless of the 71:1 value of the constant p. When 7- = 1 the series is a pseries, It converges ifp > 1 and diverges otherwise. 00 n 7. Problem: Each of the series below can be compared to a series of the form 2 . In each case, determine the best n=1 value of 1- and decide whether the series converges. A. f: (6 + navy3 \"=1 1- : . This series diverges 0 . 0 32H 7: BI Zn 313 +n9 n=1 7- : . This series converges 0 . \":1 n3 + 7 r- : . This series diverges C . 2112 + 3n + 64\" 4 D' Z ( 71+? \":1 6 + 311. + 7% r : t This series converges 0 . For each sequence an below, find a number p such that nan has a finite non-zero limit as n - co. 1 (According to the limit comparison test, the convergence or divergence of the p-series then predicts the n=1 np same behaviour for the series > an.) A. an = (7+ 5n) -5 p = 5 B. an = n' +n P = 5n2 + 5n + 5 C. an = An + 7n + 5 p = 572 + 5n + 7 8 D. an An + 7n + 5vn, p =