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:

F calc(f_a, f_b, =n = 1000)
   V r = 0.0
   L n > 0
      r = f_b(n) / (f_a(n) + r)
      n--
   R f_a(0) + r

print(calc(n -> I n > 0 {2} E 1, n -> 1))
print(calc(n -> I n > 0 {n} E 2, n -> I n > 1 {n - 1} E 1))
print(calc(n -> I n > 0 {6} E 3, n -> (2 * n - 1) ^ 2))