Sum of an Infinite Geometric Series
The sum of a geometric series having common ratio less than 1 up to infinite terms can be found. Let us derive the expression for sum as follows. We have, sum of a geometric series up to n terms given by,
Sn = a × (1 – rn)/(1 – r)
When, r<1 and n tends to infinity, rn tends to zero. Thus, above expression takes the form,
S∞ = a/(1-r)
Hence, above expression can be used to find sum of an infinite geometric progression having common ratio less than 1. Please note that above expression is valid only for geometric series having common ratio less than 1 and fails in case of common ratio being greater than 1.
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How to Find the Sum of Geometric Series
A geometric series is a sequence of numbers where each term after the first term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In a geometric series, if the absolute value of the common ratio (∣r∣) is less than 1, the series converges to a finite value. Otherwise, it diverges (grows without bound). Let’s know more about sum of Geometric Series formula, derivation and examples in detail below.
How to Find the Sum of Geometric Series
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