$$\sum_{k=1}^\infty \left(\frac{1+p}{1-p}\right)^k$$
where $p \neq 1$. I need to find the sum of this series, could anyone help me?
2026-03-26 19:03:03.1774551783
Find the sum of the series $((1+p)/(1-p))^k$
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This is a geometric series. It has a summation formula $$ \sum_{k=1}^\infty \left(\frac{1+p}{1-p}\right)^k = \frac{1+p}{1-p} \frac{1}{1-(1+p)/(1-p)} = \frac{p-1}{2p} $$ that converges if and only if $$ \left|\frac{1+p}{1-p}\right| < 1 $$