The SERIESSUM() function calculates the sum of a power series . The syntax for the function is SERIESSUM (x, n, m, coefficients). The arguments "x, n ,m ,coefficients" can be numerical values or a reference to cells.However values or feference values must be numeric otherwise the function will return a #VALUE error value. The "x" argument is the valuue of the variable x in the power series expansion. "n" is the initial power the first term is raised to, "m" is the inceremental increase in power between terms and "coefficients" is the value of the coefficients associated with each x term in the power expansion. Note: The number of terms in the power series is dependent on the number of terms in the "coefficients" argument. If there are four terms in the "coeffcients" argument then the SERIESSUM function will evelaute the power series for only four terms. The SERIESSUM function finds the sum of the power series created by the arguments "x", "n" ,"m" and "coefficients". For example SERIESSUM (1,0,1,1) = 1 and SERIESSIM (1,1,0,{1,2,4}) = 7 The power series that the Excel SERIESSUM function represents is a series that takes the form: [formula] The SERIESUM function can be modified to create many different series: e.g SERIESSUM(1,0,1,1) = 1 + 0 + 0 = 1 SERIESSUM(1,1,0,{1,2,4}) = 1 + 2 + 4 = 7 SERIESSUM(2,1,1,{1,1,1,1,1}) = 2 + 4 + 6 + 8 + 16 = 36 SERIESSUM(-0.5,1,1{1,1,1,1,1}) = - (1/2) +(1/4) - (1/8) + (1/16) - (1/32)

How to use the SERIESUM() function: Type "=SERIESSUM(". Enter the coordinate of the "x" value "1" Type a comma. Enter the coordinate of the "n" value "1". Tyep a comma. Enter the coordinate for the "m" value "1". Type a comma. Enter the coordinates for the range of "coefficients", "C2:C4". Type ")" then press the "Enter" key.

Power series can be used to approximate functions and in some cases serve as equivalent replacements these are called power series expansions. For example: e^x = 1 + x + (1/2)x^2 + (1/6)x^3 + (1/24)x^4 +....... Approimated by SERIESSUM (1,0,1{1,1,1/2,1/6,1/24}) and ln(1+x) = x - (1/2)x^2 + (1/3)(x)^3 - (1/4)(x)^4 +........ Approximated by SERIESSUM (1,1,1{1,-1/2,1/3,-1/4}) or Sin(x) = x - (1/6)(x)^3 +(1/120)(x)^5 - (1/5040)(x)^7 +........ Approximated by SERIESSUM (1,1,2,{1,-1/6,1,120,-1/5040}) For these power series to be truely equal to the corrosponding functions they must be summed to infinity. However the realy usefull thing about power series expansions is that they give extremely good apporimations of functions (when in the neighbourhood) that can be calcualted relatively easilty. This is in fact how many pocket calculators and software programs calcuate trigonometric, exponential and logarithmic function The programs base thier alogorithms on power series expansions to "evaluate" common. Of course the SERIESSUM function itself is only ever approximated to 9 decimal places the accuracy of which depends on the numbers of terms in the series to be evaluted. To learn more about power series seee [Power Series Mathematics Knowledgebase] To learn more about powerseries expansions see [Power Series Expansion Mathematics Knowledgebase]