Infinite Geometric Series Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
Find the sum: 4+2+1+12+14+⋯4 + 2 + 1 + \frac{1}{2} + \frac{1}{4} + \cdots

Solution

  1. 1
    a=4a = 4, r=12r = \frac{1}{2}. Since ∣r∣<1|r| < 1: S=41−12=412=8S = \frac{4}{1 - \frac{1}{2}} = \frac{4}{\frac{1}{2}} = 8.

Answer

88
The series halves each time. Applying the infinite geometric sum formula with a=4a=4 and r=12r=\frac{1}{2} gives 8.

About Infinite Geometric Series

The sum of all terms of a geometric sequence with common ratio ∣r∣<1|r| < 1. The infinite sum converges to a1−r\frac{a}{1-r}, where aa is the first term.

Learn more about Infinite Geometric Series →

More Infinite Geometric Series Examples

Example 1 easy

Find the sum of the infinite geometric series [formula].

Example 2 medium

Convert the repeating decimal [formula] to a fraction using an infinite geometric series.

Example 3 medium

Find the sum of the infinite series [formula]

Example 5 hard

For what values of [formula] does [formula] converge, and what is the sum?

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