Derive formula for the sum of a finite geometric series a = first term r = common ratio n = number of terms S_n = sum of first n terms S_n = a + ar + ar^2 + ... + ar^{n-1} -rS_n = -ar - ar^2 - ... - ar^{n-1} - ar^n S_n - rS_n = a - ar^n S_n(1 - r) = a(1 - r^n) S_n = a(1 - r^n) / (1 - r)
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Step 1: Start with the given sum of the first \( n \) terms of a geometric series: \[ S_n = a + ar + ar^2 + ar^3 + \ldots + ar^{n-1} \] Show more…
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