Solved Examples on Sum of Geometric Series
Example 1: Find the sum of first 5 terms of a geometric series having first term as 1 and common ratio as 2.
Solution:
We know that, sum upto n terms of a GP is given by,
⇒ Sn = a × (rn – 1)/(r – 1)
Here, a = 1, r = 2, and n = 5,
Putting all these values in the formula for Sn, we get,
⇒ Sn = 1 × (25 – 1)/(2 – 1) = 31
Thus, sum of the given series upto 5 terms is found to be 31.
Example 2: Find the sum of an infinite GP series having first term as 4 and common ratio as 1/2.
Solution:
We know that, sum of an infinite GP series is given by,
⇒ S = a/(1-r)
Here, a = 4 and r = 1/2, Putting these values in above expression,
⇒ S = 4/(1-1/2)
⇒ S = 4/(1/2) = 8
Thus, we get sum of an infinite GP series having first term as 4 and common ratio 1/2 as 8.
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.
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