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Derive the formula (1.4) for the sum S_{n} of the geometric progression S_{n} = a+ar+ar^{2}+â€¦+ar^{n-1}. Hint: Multiply S^{n} by r and subtract the result from S_{n}; then solve for S_{n}. 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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# Chapter 1 Solutions

Mathematical Methods in the Physical Sciences

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