SERIESSUM function

SERIESSUM (X, N, M, Coefficients) SERIESSUM (X; N; M; Coefficients)

X

Number Number

The input value for the power series.

N

Number Number

The power of the input value for the first term.

M

Number Number

The number that the N parameter is incremented by with each term.

Coefficients

The coefficients by which each successive power of X is multiplied. The size of this array determines the number of terms in the power series.

Returns

Number Number

The sum of the first terms of a power series.

Returns the sum of a power series. The result is INDEX (Coefficients, 1) * X ^ N + INDEX (Coefficients, 2) * X ^ (N + M) + INDEX (Coefficients, 3) * X ^ (N + 2 * M) + ... INDEX (Coefficients; 1) * X ^ N + INDEX (Coefficients; 2) * X ^ (N + M) + INDEX (Coefficients; 3) * X ^ (N + 2 * M) + .... Power series are used in many areas of mathematics, including Taylor series approximations of functions.

Examples

SERIESSUM (2, 1, 2, { 3, 5, 2 })

SERIESSUM (2; 1; 2; { 3; 5; 2 })

Returns 110. This formula is equivalent to 3 * 2 ^ 1 + 5 * 2 ^ 3 + 2 * 2 ^ 53 * 2 ^ 1 + 5 * 2 ^ 3 + 2 * 2 ^ 5, which is 6 + 40 + 64 = 1106 + 40 + 64 = 110.

SERIESSUM ( PI () / 6, 1, 2, { 1, - 1 / FACT (3), 1 / FACT (5) })

SERIESSUM ( PI () / 6; 1; 2; { 1; - 1 / FACT (3); 1 / FACT (5) })

Returns 0.5, an approximation of SIN ( PI () / 6) SIN ( PI () / 6). The Taylor series for SIN(X) is X - X ^ 3 / FACT (3) + X ^ 5 / FACT (5) - ...X - X ^ 3 / FACT (3) + X ^ 5 / FACT (5) - .... With three terms and X = PI () / 6X = PI () / 6, the result is already exactly 0.5 to four decimal places.