00 71 Consider the series E () . Evaluate the the following limit. If it is infinite, type "infinity" or \":1 arctann "inf". If it does not exist, type "DNE". 11m \" |an| = L nPCU Answer: L : D What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "lnconclusive". Answer: choose one v Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent". Answer: choose one V Assume that an+1 converges to p = =. What can you say about the convergence of the given series? an bn a ? n=1 n=1 lim bn+1 1 (Enter 'inf' for co.) 1-00 bn Can is: n=1 O A. convergent O B. divergent O C. The Ratio Test is inconclusiveSolution: given that Sbn= 9 " . an =) by = 9 . an Now , 9 anti Jim = 1-1 00 bn a " . an an . ( 9 ) . anti = lim 9. an = 9. lim an Given that, Converges to / an ie , Given , Jim anti = 2 an 8 Now , putting =) Jim buti 9 1/8 ) =" 7 1 Hence, but 1 lim 1. 12 5 n - 0o bn