Geometric Series Examples

Example 1
Find the sum of the infinite geometric series given by: .

Simplify and solve for the sum.

Locate r to make sure |r | < 1 to prove the geometric series converges.

Use the formula for the sum of an infinite geometric series.

Substitute for a _{1} and r in the formula.

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Example 2
Find the sum of the infinite geometric series given by: .

r = 3

This series diverges because |r | ≥ 1. Therefore the sum is infinite.

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Example 3
Find the sixth partial sum of the geometric series given by: .

Simplify the equation to solve for the sixth partial sum.

Use the formula for the partial sum of a geometric series.

Substitute the values you know into the formula.

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Example 4
Find the sum: .

Simplify the equation to solve for the third partial sum.

Use the formula for the partial sum of a geometric series.

Substitute the values you know into the formula.

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