4. Determine whether the following statements are true and give an explanation or counterexample. a) k=1∑∞​(eπ​)−k is a

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4. Determine whether the following statements are true and give an explanation or counterexample. a) k=1∑∞​(eπ​)−k is a convergent geometric series. b) If a is a real number and k=12∑∞​ak converges, then k=1∑∞​ak converges. c) If the series k=1∑∞​ak converges and ∣a∣<∣b∣, then the series k=1∑∞​bk converges.