Summation on HP 42S

[Thomas Klemm]

(09-23-2018 09:25 PM)lrdheat Wrote:  For something a little more complex such as summation 1 through 100 of x^2 - 3*x,

Let us rewrite this expression as:

\(\begin{align*}
x^2 - 3x &= x^2 - x - 2x \\
&= x(x-1) - 2x \\
&= 2\frac{x(x-1)}{2} -2\frac{x}{1} \\
&= 2\binom{x}{2} - 2\binom{x}{1}
\end{align*}\)

The summation leads to:

\(\sum_{x=1}^{n} 2\binom{x}{2} - 2\binom{x}{1} = 2\binom{n+1}{3} - 2\binom{n+1}{2} = 2\left ( \binom{n+1}{3}-\binom{n+1}{2} \right )\)

This program can be used to calculate the sum:

Code:

00 { 18-Byte Prgm }
01 1
02 +
03 RCL ST X
04 3
05 COMB
06 X<>Y
07 2
08 COMB
09 -
10 2
11 ×
12 END

Quote:Produces 323,200 in ~25 seconds

I haven't tested but I assume it's a bit faster than that.

Cheers
Thomas