How do you find the sum of a geometric series?

Mathematics

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A geometric series has the form a + ar + ar² + ar³ + ... where r is the common ratio. Finite sum: S_n = a(1-r^n)/(1-r). Infinite sum (when |r| < 1): S = a/(1-r). Example: 2 + 6 + 18 + 54 (a=2, r=3, n=4): S = 2(1-81)/(1-3) = 2(-80)/(-2) = 80. Infinite example: 1 + 1/2 + 1/4 + ... (r=1/2): S = 1/(1-0.5) = 2.

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A geometric series has the form a + ar + ar² + ar³ + ... where r is the common ratio.

How do you find the sum of a geometric series?
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
A geometric series has the form a + ar + ar² + ar³ + ... where r is the common ratio. Finite sum: S_n = a(1-r^n)/(1-r). Infinite sum (when |r| < 1): S = a/(1-r). Example: 2 + 6 + 18 + 54 (a=2, r=3, n=4): S = 2(1-81)/(1-3) = 2(-80)/(-2) = 80. Infinite example: 1 + 1/2 + 1/4 + ... (r=1/2): S = 1/(1-0.5) = 2.