How to find the sum of an infinite geometric series?

Solution:

Infinite geometric series is a series that has an infinite number of terms in a certain geometric pattern.

Go through the step-by-step solution to understand the formulation of the ultimate value.

The n^th term of any geometric progression = ar^(n-1)

Here, a = 1^st term, r = common multiple, n = common difference

For n tending to infinity, the formula for the sum of the series is given below.

General term of the series = ar^{(n - 1)} = T_n

Therefore, the series can be written as - a, ar, ar₂, ar₃, ar₄, ... up to infinite terms.

S_n = a + ar + ar₂ + ar₃ + ar₄ + ... up to infinite terms.

S_n = a(1 + r + r₂ + r₃ + ...)

S_n = a/(1 - r)     {Sum of an infinite geometric progression with common difference r is 1 / (1 - r)

Thus, sum of the infinite geometric progression can be solved using the formula, a(1 / 1 - r).

How to find the sum of an infinite geometric series?

Summary:

The sum of the infinite geometric progression can be solved using the formula, a(1 / 1 - r), where a is the first term and r is the common ratio.