Skip to content

Series sum

Syntax:

SERIESSUM(x, n, m, coefficients)
  • x: The input value at which the power series is evaluated. Typically, this is a numeric value.
  • n: The initial power to which x is raised.
  • m: The step by which the power increases in each term of the series.
  • coefficients: An array or range of numeric values that are multiplied by the respective powers of x.

Description:

The SERIESSUM function calculates the sum of a power series based on the input value x, the initial power n, the step m, and the provided coefficients. The power series is defined as:

SERIESSUM(x, n, m, coefficients) = c1 * (x^n) + c2 * (x^(n + m)) + c3 * (x^(n + 2*m)) + ...

Where c1, c2, ... are the values in the coefficients array.

Examples:

  1. =SERIESSUM(2, 1, 1, {1, 2, 3})
    This will calculate 1*(2^1) + 2*(2^2) + 3*(2^3), which equals 2 + 8 + 24 = 34.

  2. =SERIESSUM(0.5, 0, 1, {1, 3, 5})
    This will calculate 1*(0.5^0) + 3*(0.5^1) + 5*(0.5^2), which equals 1 + 1.5 + 1.25 = 3.75.

  3. =SERIESSUM(3, 2, 2, {2, 4})
    This will calculate 2*(3^2) + 4*(3^4), which equals 18 + 324 = 342.

Notes:

  • The coefficients array must be a valid range or an array constant (e.g., {1, 2, 3}).
  • If the coefficients array is empty, SERIESSUM will return 0.
  • Ensure the input for x, n, m, and the coefficients are numeric; otherwise, the function may return a #VALUE! error.
  • This function is particularly useful in evaluating polynomial approximations or truncated infinite series like Taylor series.