The SERIESSUM function in Google Sheets is a powerful tool for calculating the sum of a specified power series. It allows you to work efficiently with coefficients and powers, making it useful in various mathematical and financial applications. By specifying parameters for the power series, users can derive values that have significant implications in complex calculations.

Syntax

SERIESSUM(x, n, m, a)

• x: The value at which you want to evaluate the series.
• n: The exponent for the first term in the series.
• m: The step increment for the exponent in the series.
• a: A range that contains the coefficients used in the series.

Example #1

=SERIESSUM(2, 1, 1, A1:A3)

This function calculates the sum of the series using the coefficients in cells A1 to A3, evaluating at x=2 starting from n=1 and with a step size of m=1. If A1=1, A2=2, A3=3, the result would be 2^1 1 + 2^2 2 + 2^3 3 = 2 + 8 + 24 = 34.

Example #2

=SERIESSUM(3, 0, 2, B1:B4)

Here, the series sum is calculated with coefficients in B1 to B4, for x=3, starting at n=0 and stepping by m=2. For instance, if B1=1, B2=2, B3=3, B4=4, the computation would yield 3^0 1 + 3^2 2 + 3^4 3 + 3^6 4 = 1 + 18 + 162 + 972 = 1153.

Example #3

=SERIESSUM(1, 2, 1, C1:C5)

This function evaluates the power series using values in C1 to C5 at x=1 starting from an exponent of n=2 with a step increment of m=1. If C1=1, C2=2, C3=3, C4=4, C5=5, the result will be 1^2 1 + 1^3 2 + 1^4 3 + 1^5 4 + 1^6 5 = 1 + 2 + 3 + 4 + 5 = 15.

Error handling

• VALUE!: Indicates that the values provided for one or more parameters are of an incorrect data type.
• NUM!: Occurs when the input values lead to a calculation that results in an invalid number, such as a negative power with inappropriate coefficients.
• REF!: This error indicates that the range defined for the coefficient ‘a’ is invalid or refers to a non-existent cell.

Conclusion

In summary, the SERIESSUM function in Google Sheets is an essential tool for anyone looking to perform power series summations efficiently. By understanding its syntax and potential use cases, users can maximize their analytical capabilities in various fields. Whether for financial analysis, scientific research or mathematical inquiries, this function enhances productivity and precision in calculations.