Little Gauss formula for the HP15C
Description
The sum of integers up to n are calculated.
I adapted a 9 step subroutine by Torsten Manz to produce a new 7 step program. The 9 step subroutine used the original formula found by Carl Friedrich Gauss:
n n(n + 1)
∑ k = ——————————
k=1 2
This version uses the rearranged sum (n^{2} + n)/2.
g LSTx recovers n after g x².
1. Enter the number n to compute the sum of integers from 1 to n.
2. Press GSB A to run.
Example:
n = 100, (n^{2} + n)/2 = 5050.
n= 1000, (n^{2} + n)/2 = 500500.
Note that the sum is the midpoint (average) x n.
For the even number sum 1 to 10, the midpoint (average) is 5.5. The sum is 5.5 x 10 = 55.
Looking at your open hands there are usually 10 fingers  assume they represent the integers 1 to 10.
Starting to count at one thumb and ending with 10 at the other thumb, the midpoint (average) is between the little fingers, i.e at 5.5.
For the odd number sum 1 to 9, the midpoint (average) is 5. The sum is 5 x 9 = 45.
For 1 to 100 you can just average 1 and 100 or 50 and 51 = 50.5. The sum is 50.5 x 100 = 5050.
For 1 to 99 the average is 50. The sum is 50 x 99 = 4950.
Program Resources
Labels
Name 
Description 

A 
Little Gauss formula 

Program
Line 
Display 
Key Sequence 

000 



001 
42,21,11 
f LBL A 

002 
43 11 
g x² 

003 
43 36 
g LSTx 

004 
40 
+ 

005 
2 
2 

006 
10 
÷ 

007 
43 32 
g RTN 
