Derive the formula (1.4) for the sum Sn of the geometric progression Sn = a+ar+ar2+…+arn-1. Hint: Multiply Sn by r and subtract the result from Sn; then solve for Sn. Show that the geometric series (1.6) converges if and only if |r| < 1; also show that if |r| < l, the sum is given by equation (1.8).
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