State the necessary and sufficient condition for the infinite geometric series to…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

State the necessary and sufficient condition for the infinite geometric series a+ar+ar2+⋯a + ar + ar^2 + \cdots to have a finite sum. (a) ∣r∣≤1|r|\le 1 (b) ∣r∣<1|r|<1 (c) r<1r<1 (d) 0<r<10<r<1

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