here is what you should do

1 Purpose

This program introduces the need for design of a simple algorithm which can perhaps be best

completed with a set of auxiliary functions. The design and implementation will provide the

student with practice in function declaration, denition and use. The required computations also

demand care in data type manipulation.

2 Procedure

1. Your task is to write a C++ program which computes the approximation of by a series

summation known as the MadhavaLeibniz series. A concise overview is provided on the

following web link:

http://en.wikipedia.org/wiki/Leibniz formula for pi

USE LINK FOR THE FORMULA

The formula is given as follows:

= 4

1X

k=0

(????1)k

2k + 1

2. Your program should prompt the user for one integer, the largest value of the index k in

the truncated summation of the formula.

(a) NOTE: your program should demand that the value input be nonnegative. More

specically, it should continue to prompt for a value until an integer equal to or greater

than 0 is entered.

(b) The result should be displayed to at least 10 digits to the right of the decimal point.

(d) A text..Prog05Test.txt which contains demonstration dialog of your programs

behavior.

Insert comments in this le regarding the validity of your results (for example, demon-

strate that the user inputs are handled as prescribed above, and that as you increase

the maximum value of k, the computed result approaches the value of , which we can

nd in many resources, to be as follows (at least to 15 digits of precision). . . )

3.141592653589793

An example of the test le for this programming assignment would be as follows:

**HERE IS WHAT THE PROGRAM SHOULD LOOK LIKE**

** **

V:TMP> Prog05

Computing pi Series Summation by ML Formula // KB: This term is easy to check.

============++++++++++=====================

Enter maximum value of k in truncated series (non-negative): 0

Approximation of pi is 4.000000000000000

V:TMP> Prog05

Computing pi Series Summation by ML Formula // KB: disallows negative inputs.

============++++++++++=====================

Enter maximum value of k in truncated series (non-negative): -9

Enter maximum value of k in truncated series (non-negative): -1

Enter maximum value of k in truncated series (non-negative): 1

Approximation of pi is 2.666666666666667

V:TMP> Prog05

Computing pi Series Summation by ML Formula

============++++++++++=====================

Enter maximum value of k in truncated series (non-negative): 50

Approximation of pi is 3.161198612987051

V:TMP> Prog05

Computing pi Series Summation by ML Formula

============++++++++++=====================

Enter maximum value of k in truncated series (non-negative): 100

Approximation of pi is 3.151493401070991

V:TMP> Prog05

Computing pi Series Summation by ML Formula // KB: slowly approaching pi!

============++++++++++===================== // KB: theres a better series!

Enter maximum value of k in truncated series (non-negative): 10000

Approximation of pi is 3.141692643590535

V:TMP>

Subject | Computer |

Due By (Pacific Time) | 09/27/2013 10:00 pm |

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