$k + (k-1)/2 + (k-2)/4 + ....$ so on.
What is the method to solve this series? Since, it seems to have both AP and GP, I'm unsure how to solve it.
2026-03-26 17:33:34.1774546414
How to solve a series in which part of the term is in AP and other part is in GP?
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The series rewrites as $$\frac{k}{1} + \frac{k}{2}-\frac{1}{2}+\frac{k}{4}-\frac{1}{2}+\frac{k}{8}-\frac{1}{2}+\cdots$$ However the odd-indexed terms are $$\frac{k}{1}+\frac{k}{2}+\frac{k}{4}+\cdots = 2k$$ Since those converge absolutely, the convergence of the original series depends on the convergence of the even-indexed terms, namely $$-\frac{1}{2}-\frac{1}{2}-\frac{1}{2}-\cdots$$ which diverge.