(48SX and 12C): Continued Fractions

[Eddie W. Shore]

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