Math 153 Concept Check 05 Problem 1) What can you conclude about each of the following series using the Divergence Test? Put a check mark in the box next to the right answer. 3 a) E (a) _ You can conclude that the series converges using the Divergence Test. _ You can conclude that the series diverges using the Divergence Test. _ You cannot make any conclusion about the series using the Divergence Test. 2 n b) E (- 5) You can conclude that the series converges using the Divergence Test. You can conclude that the series diverges using the Divergence Test. You cannot make any conclusion about the series using the Divergence Test. C] E 3n23n You can conclude that the series converges using the Divergence Test. You can conclude that the series diverges using the Divergence Test. You cannot make any conclusion about the series using the Divergence Test. d} z 1111(1) You can conclude that the series converges using the Divergence Test. You can conclude that the series diverges using the Divergence Test. You cannot make any conclusion about the series using the Divergence Test. Problem 2} Consider a sequence an. You don't know everything about the values of this sequence, but you do know the following two facts: 0 If n is divisible by 4 (e.g. n = 0, 4, 8, 12...), then an = 1%. o lfn has a remainder of 2 when divided by4 (e.g. n = 2, 6, 10, 14...] then at,1 = 1 2%. Is it possible for the series 2 a,1 to converge? Explain your