Saturday, April 18, 2020

HP 12C: Sums of x

HP 12C:  Sums of x

Introduction

The following are four programs to calculate:

*  ∑ x
*  ∑ x^2
*  ∑ x^3
*  ∑ ax + b

with limits x = 0 to n.

Each program uses a closed sum formula.  The second and fourth program uses Horner's Method. 

Note:  You can use the first three if your limits are x = 1 to n (because at x = 0, 0 is added to the sum).  However if you use the fourth program, to get the sum from 1 to n, subtract b. 

HP 12C Program:  ∑x (x=0 to n)

n
∑ x =  n * (n + 1) / 2
x=0

Enter n, execute program

STEP:  KEY CODE  KEY
01:  36  ENTER
02:  36  ENTER
03:  1  1
04:  40  +
05:  20  *
06:  2   2
07  10  ÷
08:  43,33,00  GTO 00

Keys Only:
ENTER
ENTER
1
+
2
*
÷
GTO 00

Example:  (n = 48)

48
∑ x  = 1176
x=0

HP 12C Program:  ∑x^2 (x=0 to n)

n
∑ x^2 =  n * ( ( n / 3 + 1 / 2 ) * n + 1 / 6 )
x=0

Enter n, execute program

STEP:  KEY CODE KEY
01:  36  ENTER
02:  36  ENTER
03:  36  ENTER
04:  3  3
05:  10  ÷
06:  2  2
07:  22  1/x
08:  40  +
09:  20  *
10:  6  6
11:  22  1/x
12:  40  +
13:  20  *
14:  43,33,00  GTO 00

Keys Only:
ENTER
ENTER
ENTER
3
÷
2
1/x
+
*
6
1/x
+
*
GTO 00

Example:  (n = 48)

48
∑ x^2  = 38,024
x=0

HP 12C Program:  ∑x^3 (x=0 to n)

n
∑ x^3 =  1 / 4 * (n^2 + n)^2
x=0

Enter n, execute the program

STEP:  KEY CODE  KEY
01:  36  ENTER
02:  36  ENTER
03:  2  2
04:  21  y^x
05:  40  +
06:  2:  2
07:  21  y^x
08:  4  4
09:  10  ÷
10:  43,33,00  GTO 00

Keys Only:
ENTER
ENTER
2
y^x
+
2
y^x
4
÷
GTO 00

Example:  (n = 32)

32
∑ x^3  = 278,784
x=0

HP 12C Program:  ∑(a*x + b)  (x=0 to n)

n
∑ (a*x + b) =  n * (a * n / 2 + (a / 2 + b) ) + b
x=0

Store a in R1, store b in R2, enter n on the x-stack, execute the program

STEP:  KEY CODE   KEY
01:  36   ENTER
02:  36   ENTER
03:  36   ENTER
04:  45, 1  RCL 1
05:  20   *
06:  2    2
07:  10   ÷
08:  45, 1  RCL 1
09:  2   2
10:  10   ÷
11:  45, 2   RCL 2
12:  40   +
13:  40   +
14:  20   *
15:  45, 2  RCL 2
16:  40  ÷
17:  43, 33, 00   GTO 00

Keys Only:
ENTER
ENTER
ENTER
RCL 1
*

÷
RCL 1
2
÷
RCL 2
+
+
*
RCL 2
÷
GTO 00

Example:  (a = R1 = 3,  b = R2 = 4, n = 32)

3 STO 1,  4 STO 2,  32, R/S

32
∑ (3x + 4) = 1,716
x=0


I tried something new with my RPN keystroke programs, the second versions of each I just listed what keys to press without the step number or code.  I think this would be easier to read, but does leave out the key and key code.  Any comments on which style is preferred is appreciated. 


Eddie

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