4. July is working on some series practice problems. In each part, decide whether his solution is reasoned correctly. If it isn't, explain exactly what is wrong with July's reasoning. (Remember that we want you to evaluate July's reasoning, which may be incorrect even if his nal conclusion is correct.) 00 2 (a) Decide whether the series 2 sin (616) converges. Explain your reasoning. k=1 2 July's answer: As k: > oo, 63,, > 0. This implies that sin (ek) > sin(0) = 0. Therefore, the series converges by the Nth Term Test. 00 2 (b) Decide whether the series 2 cos (tik) converges. Explain your reasoning. k=1 2 July's answer: As k > oo, 6% > 0. This implies that cos (Isk) > cos(0) = 1. Therefore, the series diverges by the Nth Term Test