(12C Platinum) Sums of Powers of N numbers

[Thomas Klemm]

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
02-      24    ∆%
03-   44 12    STO i
04-   42 13    NPV

1. Arithmetic Series

\(\frac{x(x+1)}{2}=\frac{x^2}{2}+\frac{x}{2}\)

0
CF₀
2 1/x
CF_i
CF_i


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
CF_i
2 1/x
CF_i
3 1/x
CF_i


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
CF_i
4 1/x
CF_i
2 1/x
CF_i
x<>y
CF_i


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