(a) (b) (C) (0 Demonstrate that the integral If\" 33%, d2: convergent for p > 1 but not for p g 1. Read about the Ratio Test in Boas and Show that based on that test you cannot conclude for which p the sum 2,2: is convergent or divergent. Read about the Integral1 Test (Boas Sec 1. 6. B). Show (hint: be inspired by Fig 6.1 in Boas) that the integral 1001 1$+1)p dz: is a lower bound on the sum 2:1ip and use it to argue that the series 211:1 11111, is divergent for p S 1. 1 Now argue that I100 3311, d2: gives and upper bound on the series 22:1 E and use that to argue that the series is convergent for p > 1. BONUS. The Riemann zeta function is dened as 1 :2 g (1) n=1 For integer and even p, ((10) is propertional to 771). Look up the values of ((2) and ((4) and compare them to the upper bound you found in (d). BONUS. Consider Sp : ((39) as a sequence for p : 2, 3, 4, . . .. Can you derive a limiting value of C(p) as p > oo