Practice Problems on Sum of Geometric Series
Problem 1: Find sum of the series: 4, 12, 36, 108, . . . up to 6 terms.
Problem 2: Find sum of the infinite series: 64, 16, 4, 1, . . . up to infinite terms.
Problem 3: Find sum of a GP having first term a = 5 and common ratio = 2 up to 7 terms.
Problem 4: What would be sum of a GP series having a = 1 and common ratio = 1/2 up to 5 terms.
Problem 5: Determine the sum: 40 + 10 + 2.5 + up to infinite terms.
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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