1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n 2 1). Let f be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions. (a) If > (an + an+1) is convergent, then E an is convergent. n=1 n=1 Final Answer This claim is TRUE FALSE.(c) If the series E an is convergent, then M sin(an + n is convergent . n=1 n=1 Final Answer This claim is TRUE FALSE.(d) If the series 2 an is divergent, then 2 71:1 n21 an 1 + an is divergent. Final Answer This claim is TRUE FALSE. OO (e) If the series an is convergent, then In 3 + an is convergent. 3 + an+1 n=1 n=1 Final Answer This claim is TRUE FALSE.00 00 (f) If the series 2 an is convergent, then 2M1; f (Los(n))] is convergent. n21 1121 Final Answer This claim is TRUE FALSE. (g) If the series E an is convergent, then (-1)" Van is convergent. n=1 n=1 Final Answer This claim is TRUE FALSE.DC 00 (b) If the series 2 an is convergent} then 2 arctan + an) is divergent. n=1 \"=1 Final Answer This claim is TRUE FALSE