Sunday, August 9, 2020

HP 12C: Last X: Sums and Products

HP 12C:   Last X:   Sums and Products

Introduction

It is possible to use the LST X feature on the HP 12C calculators assist us in quickly calculate sums or products  of a terms, especially when the list of terms are in a series. 

For today's blog, we are starting with a base amount, a, and then adding 1 to each term.   You can use a similar algorithm for a sequence where each term is doubled, tripled, 1 is subtracted from the previous term, and so on.  The key is to complete the adjustment, use storage arithmetic, and then use LST X.

Accessing LST X:

HP 12C (Classic):  [ g ] [ ENTER ]

HP 12C Platinum:  [ g ] [ + ]

These algorithms can be used in program. 


Sum:  a + (a+1) + (a+2)  + (a+3) + ....

Let n represent the storage register to be used.  On the HP 12C, only storage registers R0 through R4 (classic HP 12C).

Algorithm:


STO n

Loop:  
LST X 
1     [ or 2, x  to double each term,  1, - to subtract 1, etc.]
+  
STO+ n    [stores what is in the X display to the Last X register]

Finish:  
RCL n


Example:  7 + 8 + 9 +10 = 34.   Use register 0 to store the sum.

7
STO 0

LST X
1
+
STO+ 0

LST X
1
+
STO+ 0

LST X
1
+
STO+ 0

RCL 0


Sum:  1/a + 1/(a+1) + 1/(a+2) + 1/(a+3) + ....

Algorithm:


1/x
STO n

Loop:  
LST X 
1     
+  
1/x
STO+ n    

Finish:  
RCL n

Example:  1/7 + 1/8 + 1/9 + 1/10 ≈ 0.47897

7
1/x
STO 0

LST X
1
+
1/x
STO+ 0

LST X
1
+
1/x
STO+ 0

LST X
1
+
1/x
STO+ 0

RCL 0

Sum:  √a + √(a+1) + √(a+2) + √(a+3) + ...

Algorithm:



STO n

Loop:  
LST X 
1     
+  

STO+ n    

Finish:  
RCL n

Try the algorithm on this example:  √7 + √8 + √9 + √10 ≈ 11.63646

Sum:  a^2 + (a+1)^2 + (a+2)^2 + (a+3)^2 + ...

Hint:  Use ENTER, x instead of 2, y^x

Algorithm:


ENTER 
*
STO n

Loop:  
LST X 
1     
+  
ENTER
*
STO+ n    

Finish:  
RCL n

Try the algorithm on this example:  7^2 + 8^2 + 9^2 + 10^2 = 294

Let's move on to products.

Product:  a * (a+1) * (a+2) * (a+3) * ....


STO n

Loop:  
LST X 
1     
+  
STOx n    

Finish:  
RCL n


Example:  7 * 8 * 9 * 10 = 5040.   Use register 0 to store the product.

7
STO 0

LST X
1
+
STOx 0

LST X
1
+
STOx 0

LST X
1
+
STOx 0

RCL 0

Product:  1/a * 1/(a+1) * 1/(a+2) * 1/(a+3) * ....


1/x
STO n

Loop:  
LST X 
1     
+  
1/x
STOx n    

Finish:  
RCL n


Try the algorithm on this example 1/7 * 1/8 * 1/9 * 1/10 ≈ 0.0020

Product:  √a * √(a+1) * √(a+2) * √(a+3) * .......



STO n

Loop:  
LST X 
1     
+  

STOx n    

Finish:  
RCL n


Try the algorithm on this example √7 * √8 * √9 * √10 ≈ 70.99296

Hopefully this will help your calculations on your RPN calculators faster and more effective,

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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