Explain how to find the sum of an infinite geometric series.

To find the sum of an infinite geometric series, use the formula S = a/(1-r), where a is the first term and r is the common ratio.

An infinite geometric series is a series where each term is multiplied by a constant ratio to get the next term, and this pattern continues infinitely. The sum of an infinite geometric series can be found using the formula S = a/(1-r), where a is the first term and r is the common ratio.

To use this formula, first determine the values of a and r. Then substitute these values into the formula and simplify. For example, consider the series 2 + 4 + 8 + 16 + ... . Here, a = 2 (the first term) and r = 2 (the common ratio). Substituting these values into the formula, we get:

S = 2/(1-2)
S = 2/-1
S = -2

Therefore, the sum of the infinite geometric series 2 + 4 + 8 + 16 + ... is -2.

It is important to note that the formula S = a/(1-r) only works if the absolute value of r is less than 1. If the absolute value of r is greater than or equal to 1, the series does not have a sum. In this case, the series is said to diverge.