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Geometric Sequencesmedium
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Consider the series ∑n=1∞arn−1\sum_{n=1}^{\infty} a r^{n-1}∑n=1∞​arn−1. If the sequence of partial sums SnS_nSn​ satisfies Sn+1=2Sn+1S_{n+1} = 2S_n + 1Sn+1​=2Sn​+1, is the sequence geometric?