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+--- Thread: (48SX and 12C): Continued Fractions (/thread-17909.html)
(48SX and 12C): Continued Fractions - Eddie W. Shore - 01-09-2022 07:23 PM
Continued Fractions
A continued fraction is a nested fraction in the form, shown in a linear fashion:
a_0 + 1 ÷ (a_1 + 1 ÷ (a_2 + 1 ÷ (a_3 + 1 ... ÷ (a_n-1 + 1 ÷ a_n ) ... )
Below are two examples of continued fractions:
Example 1: 5 + 1 ÷ (3 + 1 ÷ 7)
Example 2: 6 + 1 ÷ (4 + 1 ÷ (2 + 1 ÷ 5))
HP 48GX Program: CNFRC
Instructions:
1. Clear the stack.
2. Enter values from a_0, a_1, a_2, to a_n.
3. Run CNFRC
Program:
Code:
<< DEPTH 1 - 1 SWAP START INV + NEXT EVAL >>Example 1 (refer to the above):
Input: Clear the stack, 5, ENTER, 3, ENTER, 7, run CNFRC
Output: 5.31818181818
Example 2 (refer to the above):
Input: Clear the stack, 6, ENTER, 4, ENTER, 2, ENTER, 5, run CNFRC
Output: 6.22448979592
HP 12C Program: Continued Fractions
1. Enter a_n, ENTER a_n-1
2. Press [ R/S ]
3. Work backwards, enter a_n-2, press [ R/S ] until the end
Program: (step, key code, key)
Code:
01 34 x<>y
02 22 1/x
03 40 +
04 43,33,00 GTO 00**43,33,000 GTO 000 for HP 12C Platinum
For the examples, the HP 12C set to FIX 5
Example 1 (refer to the above):
Input: 7, ENTER, 3, R/S, 5, R/S
Output: 5.31818
Example 2 (refer to the above):
Input: 5, ENTER, 2, R/S, 4, R/S, 6, R/S
Output: 6.22449