Thank you. Looks fine. Leibniz would be happy.

:)

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Write a program that Calculate the value of π

from the infinite series

Print a table that shows the value of π approximated

by one term of this series, by two terms, by three

terms, and so on.

**What I have tried:**

from the infinite series

Print a table that shows the value of π approximated

by one term of this series, by two terms, by three

terms, and so on.

Output: Accuracy set at: 40 term pi 1 4.000000 2 2.666667 3 3.466667 4 2.895238 5 3.339683 6 2.976046 7 3.283738 8 3.017072 ... ... ... 40 3.116597

C#

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace picalc { class Program { static void Main(string[] args) { int accuracy; double piValue = 0; double numerator = 4.0; double denominator = 1.0; Console.Write("Enter the number of terms:"); accuracy = Convert.ToInt32(Console.ReadLine()); int i; Console.WriteLine("Term \t\tPi"); for (i = 1; i <= accuracy; i++) { double x = (numerator / denominator); if ((i % 2) == 0) { piValue -= x; } else { piValue += x; } denominator += 2.0; Console.WriteLine("{0}\t\t{1:F16}", i, piValue); } Console.ReadLine(); } } }

Comments

Patrice T
30-Dec-21 10:32am

And you have a question ?

Shams Imad
30-Dec-21 11:13am

yes,How can this question be solved?

Thank you. Looks fine. Leibniz would be happy.

:)

:)

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Comments

Shams Imad
30-Dec-21 11:14am

How can this question be solved?

Luc Pattyn
30-Dec-21 11:30am

I see one way to improve your code:

rather than asking the user how many iterations he wants (what you erroneously call "accuracy"), you could let the loop continue until the difference drops below a specified tolerance, say 1e-12

It then would be wise not to show all intermediate steps...

:)

rather than asking the user how many iterations he wants (what you erroneously call "accuracy"), you could let the loop continue until the difference drops below a specified tolerance, say 1e-12

It then would be wise not to show all intermediate steps...

:)

Shams Imad
30-Dec-21 11:32am

Can you write the code to solve this question?

Luc Pattyn
30-Dec-21 11:58am

Writing the code is your job, not mine.

You're on track; see my suggestion in my previous reply to you.

:)

You're on track; see my suggestion in my previous reply to you.

:)

Shams Imad
30-Dec-21 11:59am

I don't understand, can you explain to me your previous comment?

Luc Pattyn
30-Dec-21 12:08pm

Your pi approximations are slightly above, then slightly below, the correct value, as you alternately add/subtract a correction term. So it would be best to keep iterating until said correction becomes irrelevantly small, i.e. less than epsilon, which is a small number that must satisfy the relationship

which means it is still noticeable when using a number representation with finite precision. As

NB: that will take billions of iterations, since

1.0 + epsilon != 1.0

which means it is still noticeable when using a number representation with finite precision. As

`double`

is capable of holding about 15 decimals, epsilon = 10^-12 seems very reasonnable. That would give a pi approximation with some 12 correct digits.NB: that will take billions of iterations, since

`denominator`

only grows by 2 per iteration!Quote:Write a program that Calculate the value of π from the infinite series

As programmer, your job is to create solutions to given problems, as student, this homework is training/practicing and all homework makes early experience.

First of all you need to get informations about known methods to calculate pi with infinite decimals: Infinite Expressions for Pi[^]

If you take the pain to search internet, you will find pieces of code that do the job.

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