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:

numfmt 8 0
func calc_sqrt .
   n = 100
   sum = n
   while n >= 1
      a = 1
      if n > 1
         a = 2
      .
      b = 1
      sum = a + b / sum
      n -= 1
   .
   return sum
.
func calc_e .
   n = 100
   sum = n
   while n >= 1
      a = 2
      if n > 1
         a = n - 1
      .
      b = 1
      if n > 1
         b = n - 1
      .
      sum = a + b / sum
      n -= 1
   .
   return sum
.
func calc_pi .
   n = 100
   sum = n
   while n >= 1
      a = 3
      if n > 1
         a = 6
      .
      b = 2 * n - 1
      b *= b
      sum = a + b / sum
      n -= 1
   .
   return sum
.
print calc_sqrt
print calc_e
print calc_pi