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PrecalculusMediumSequences, Series, and the Binomial Theorem

Sequences, Series, and the Binomial Theorem · Medium problem

Evaluate the infinite geometric series ∑k=1∞3(−25)k−1\displaystyle\sum_{k=1}^{\infty} 3\left(-\tfrac{2}{5}\right)^{k-1} (it converges because ∣r∣<1|r|<1).