Explain why or why not Determine whether the
Chapter 11, Problem 59E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. \(\sum_{k=1}^{\infty}\left(\frac{\pi}{e}\right)^{-k}\) is a convergent geometric series.
b. If a is a real number and \(\sum_{k=12}^{\infty} a^{k}\) converges, then \(\sum_{k=1}^{\infty} a^{k}\) converges.
c. If the series \(\sum_{k=1}^{\infty} a^{k}\) converges and |a| < |b|, then the series \(\sum_{k=1}^{\infty} b^{k}\) converges.
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