(12C Platinum) Sums of Powers of N numbers
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01-22-2019, 11:57 PM
Post: #4
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RE: (12C Platinum) Sums of Powers of N numbers
We can use the Net Present Value (NPV) to evaluate a polynomial:
\(NPV = CF_0 + \frac{CF_1}{1+r} + \frac{CF_2}{(1+r)^2} + \frac{CF_3}{(1+r)^3} + \cdots + \frac{CF_n}{(1+r)^n}\) Use the ∆% function to transform \(x=\frac{1}{1+r}\) to \(i=100r\). This leads to the following generic program to evaluate a polynomial: Code: 01- 1 1 1. Arithmetic Series \(\frac{x(x+1)}{2}=\frac{x^2}{2}+\frac{x}{2}\) 0 CF0 2 1/x CFi CFi Examples: 1 R/S 1.0000 2 R/S 3.0000 3 R/S 6.0000 10 R/S 55.0000 2. Sum of the consecutive Squares \(\frac{x(x+1)(2x+1)}{6}=\frac{x^3}{3}+\frac{x^2}{2}+\frac{x}{6}\) 0 CF0 6 1/x CFi 2 1/x CFi 3 1/x CFi Examples: 1 R/S 1.0000 2 R/S 5.0000 3 R/S 14.0000 10 R/S 385.0000 3. Sum of the consecutive Cubes \(\frac{x^2(x+1)^2}{4}=\frac{x^4}{4}+\frac{x^3}{2}+\frac{x^2}{4}\) 0 CF0 CFi 4 1/x CFi 2 1/x CFi x<>y CFi Examples: 1 R/S 1.0000 2 R/S 9.0000 3 R/S 36.0000 10 R/S 3025.0000 Disclaimer: I don't have an HP-12C Platinum. But this works with the regular HP-12C. Kind regards Thomas PS: Cf. HP-12C’s Serendipitous Solver |
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