Problem Statement

The task is to write a program which generates such a number and prints a real representation of it. The code should be tested by calculating and printing the square root of 2, Napier's Constant, and Pi, using the following coefficients: For the square root of 2, use

a

0

= 1

{\displaystyle a_{0}=1}

then

a

N

= 2

{\displaystyle a_{N}=2}

.

b

N

{\displaystyle b_{N}}

is always

1

{\displaystyle 1}

. For Napier's Constant, use

a

0

= 2

{\displaystyle a_{0}=2}

, then

a

N

= N

{\displaystyle a_{N}=N}

.

b

1

= 1

{\displaystyle b_{1}=1}

then

b

N

= N − 1

{\displaystyle b_{N}=N-1}

. For Pi, use

a

0

= 3

{\displaystyle a_{0}=3}

then

a

N

= 6

{\displaystyle a_{N}=6}

.

b

N

= ( 2 N − 1

)

2

{\displaystyle b_{N}=(2N-1)^{2}}

.

Let's start with the solution:

# Project : Continued fraction

see "SQR(2) = " + contfrac(1, 1, "2", "1") + nl
see "        e = " + contfrac(2, 1, "n", "n") + nl
see "       PI = " + contfrac(3, 1, "6", "(2*n+1)^2") + nl

func contfrac(a0, b1, a, b)
        expr = ""
        n = 0
        while len(expr) < (700 - n)
                 n = n + 1
                 eval("temp1=" + a)
                 eval("temp2=" + b)
                 expr = expr + string(temp1) + char(43) + string(temp2) + "/("
        end 
        str = copy(")",n)
        eval("temp3=" + expr + "1" + str)
        return a0 + b1 / temp3