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