About Infinite Series Formula
The infinite series formula is used to calculate the sum of a sequence with an unlimited number of terms. Infinite series come in a variety of shapes and sizes. The sum of infinite arithmetic series and the sum of infinite geometric series will be discussed in this section. The arithmetic series is one in which the difference between each successive term remains constant throughout, whereas the geometric series is one in which the ratio of subsequent terms to the preceding term remains constant throughout. An infinite series formula is a useful tool for quickly calculating the total.
What do you mean by Infinite Series Formula?
To find the sum of a series that extends to infinity, use the sum of the infinite geometric series formula. The sum of infinite GP is another name for this. Even though the series has infinite terms, we discover that the sum of a GP converges to a value. If -1 < r < 1, the infinite series formula is as follows:
- Sum = a/(1-r)
- Here, a is the first term of the series, r is the common ratio between two consecutive terms and −1 < r < 1
- Note: If r > 1, the sum does not exist as the sum does not converge.
- Sum of an infinite arithmetic sequence is ∞, if d > 0, or
- Sum of an infinite arithmetic sequence is ∞, if d > 0 - ∞ , if d < 0.
Solved example of Infinite Series Formula
Example: Using an infinite series formula, find the sum of infinite series: +?
- Sol: It is given that a = and r = (1/16) / (1/4) = (1/64) / (1/16) =
- To find out the Sum of given infinite series
- If r<1 is then sum is given as Sum = a/(1-r)
- Applying the values to the infinite series formula, we get
- Sum = (1⁄4)/(1-1⁄4)
- Sum = (1⁄4)/(3⁄4)
- Sum = 4/(3 × 4)
- Sum = 1/3
- Answer: The sum of 1/4+1/16+1/64+1/256+? is 1/3
Maths Formulas prepared by HT experts are listed on the main page.
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