Evaluate Infinite Geometric Series with \( \frac{1}{1 + \sqrt{2}} \)

Math Problem Statement

Evaluate the infinite series: \( \sum_{n=1}^{\infty} \left( \frac{1}{1 + \sqrt{2}} \right)^{n-1} \)

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Series
Infinite Geometric Series

Sum of an infinite geometric series: \( S = \frac{a}{1 - r} \) where \( |r| < 1 \)

Geometric Series Sum Formula

Grades 10-12

Evaluate the Infinite Series \( \sum_{n=1}^{\infty} \left( \frac{1}{1 + \sqrt{2}} \right)^{n-1} \) - Solution and Explanation

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