CSCI 111 UCF Chapter 7 Program 5 Approximation to ? Project I uploaded the assignment in pdf and i hope u do a great job on it.—————————-
CSCI 111 UCF Chapter 7 Program 5 Approximation to ? Project I uploaded the assignment in pdf and i hope u do a great job on it.——————————- Chapter 7: Program 5 – Approximation to ?
CSCI111: Introduction to Computing
Assigned: Friday, April 3, 2020
Due: Friday, April 10, 2020 at midnight on Blackboard
Consider the following function.
1
?
where a(k) =
=
?
2 2
(a(0) + a(1) + a(2) + . . .)
9801
(4k)!(1103 + 26390k)
.
(k!)4 3964k
This gives
? ?
1
2 2 X (4k)!(1103 + 26390k)
.
=
?
9801
(k!)4 3964k
k=0
The notation n! indicates a factorial. In general n! = n(n ? 1)(n ? 2) · · · (2)(1) and 0! = 1 by definition. Python computes factorials by using a function from the math library. So, for example, 5! =
math.factorial(5). So you will need to import math in your program.
Requirements for this program are as follows:
1. Your program must include a comment header with Author, Assignment (Program 5), Description,
and Due Date
2. Write a function to compute a general term in the sum. The function should allow an integer argu(4k)!(1103 + 26390k)
ment, k. Call the function A and it should return the value given by:A(k) =
(k!)4 3964k
3. Write a function called pi recip. The function should use a while loop to sum the terms, (A), until
?
2 2
the last term of the sum is less than 10?15 . Once the sum is done, it should be multiplied by 9801
.
4. Use the result of pi recip to get an approximation for ?.
5. Print with clear explanation the computed estimate of ? and Pythons version of ? which is math.pi.
6. Your program that you submit must be a script in a file named program5 WillM.py where you
replace WillM with your first name and last initial.
7. Submit just that program on Blackboard under Chapter 7, Program 5.
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