Little Gauss for the HP-15C

Description

This program computes the sum of the numbers between 1 and a given integer n.

A problem well known as 'Little Gauss'. Ask your preferred Internet search engine if you have not heard about 'Little Gauss'.

The program provides two solutions for the problem. First a brute force algorithm adding one number after the other. This version uses the internal HP-15C function ISG. Secondly the program provides the original formula found by Carl Friedrich Gauss:


n n(n + 1)
k = ——————————
k=1 2


1. Enter the number n, for which you want to compute the Gauss sum.
2. Press f A to run the ISG version
or
press f B to run the original formula.

Due to the limitations of the ISG function, n must be less than 1000 when using this version.

Program Resources

Labels

Name Description
 A Little Gauss using built in function ISG
 B Little Gauss using the formula
 1 Start of ISG sub program
 2 Sub program to sum up the numbers
 3 Set flag 9 (blinking) in case of error

Storage Registers

Name Description
 0 Cumulated sum
 1 Counter for ISG function

Flags

Number Description
9 Flag 9 is set if the integer number is greater than 999 when using the ISG version.

Program

Line Display Key Sequence Line Display Key Sequence
000 021 42. 6. 1 f ISG 1
001 42.21.11 f LBL A 022 22 2 GTO 2
002 9 9 023 45 0 RCL 0
003 9 9 024 43 32 g RTN
004 9 9 025 42.21. 2 f LBL 2
005 43.30. 8 g TEST x<y 026 45 1 RCL 1
006 22 3 GTO 3 027 43 44 g INT
007 42 34 f REG 028 44.40. 0 STO + 0
008 34 x↔y 029 22 1 GTO 1
009 1 1 030 42.21. 3 f LBL 3
010 26 EEX 031 43. 4. 9 g SF 9
011 3 3 032 43 32 g RTN
012 16 CHS 033 42.21.12 f LBL B
013 20 × 034 36 ENTER
014 1 1 035 36 ENTER
015 26 EEX 036 1 1
016 5 5 037 40 +
017 16 CHS 038 20 ×
018 40 + 039 2 2
019 44 1 STO 1 040 10 ÷
020 42.21. 1 f LBL 1 041 43 32 g RTN