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:

10 LET a0=1: LET b1=1: LET a$="2": LET b$="1": PRINT "SQR(2) = ";: GO SUB 1000
20 LET a0=2: LET b1=1: LET a$="N": LET b$="N": PRINT "e = ";: GO SUB 1000
30 LET a0=3: LET b1=1: LET a$="6": LET b$="(2*N+1)^2": PRINT "PI = ";: GO SUB 1000
100 STOP 
1000 LET n=0: LET e$="": LET p$=""
1010 LET n=n+1
1020 LET e$=e$+STR$ VAL a$+"+"+STR$ VAL b$+"/("
1030 IF LEN e$<(4000-n) THEN GO TO 1010
1035 FOR i=1 TO n: LET p$=p$+")": NEXT i
1040 PRINT a0+b1/VAL (e$+"1"+p$)
1050 RETURN