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<strong>Infinite</strong> <strong>Series</strong> <strong>Notes</strong>, <strong>Teacher</strong>.<strong>notebook</strong>January 09, 2013Question: Does the method for finding the partial sums ofthe three series in the first example involve recursion?Explain.<strong>Infinite</strong> Geometric <strong>Series</strong>For any infinite geometric series with , the terms getcloser and closer to zero. This means that infinite geometricseries will have a sum ifThe general formula for the sum S or S n of aninfinite geometric series, a 1 + a 2 + . . . with common ratio rwhere is:Example 2: Decide whether the following series has asum. If it does, give its value.Sigma Notation with <strong>Infinite</strong> <strong>Series</strong>To write an infinite series in sigma notation, use the symbolfor infinity. In sigma notation, the infinite serieslooks like this:2
<strong>Infinite</strong> <strong>Series</strong> <strong>Notes</strong>, <strong>Teacher</strong>.<strong>notebook</strong>January 09, 2013Example 3: Evaluate the following if the sum exists.Question: How can you use partial sums to find the sumof an infinite series?3
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