can someone help me to figure this out >.<

IT 112/ ICS 112 Midterm Laboratory Exercise Set 01

Problem 1: (GregorySeriesLimit.java)

The number “pi” (3.14159...) can not be expressed as a simple ratio of two numbers. Instead, the value of pi is typically calculated by summing up the terms of an infinite number series. As more and more terms in the series are evaluated, the sum approaches the “true” value of pi. One series that can be used for this purpose is called the Gregory series, which computes the value of pi as follows:

pi = 4/1 – 4/3 + 4/5 – 4/7 + 4/9 – 4/11 + …

Observe that the numeric values of the terms of the series get smaller and smaller as the calculation progresses. For example, the value of the 1st term is 4/1 = 4, the 2nd term is 4/3 = 1.333…, the 3rd term is 4/5 = 0.8, and so on.

Write a program that calculates the value of pi using the Gregory series. The input to the program will be a decimal value called limit. The program shall proceed to calculate the value of pi by summing up the terms of the series, but only until such time that the value of the term being summed becomes less than or equal to the value of limit, at which point the program terminates the summation. Thus, the last term of the series that is added to the sum is the first term whose value is less than or equal to the value of limit.

The program then prints out the calculated value of pi at that point, as well asthe actual number of terms that were summed up by the calculation.

SAMPLE OUTPUT:

1.) Input Limit: 0.005

Calculated Value of PI: 3.1659792728432157

No. of Terms Summed: 41

2.)Input Limit: 0.00001

Calculated Value of PI: 3.141597653564762

No. of Terms Summed: 200001

3.)Input Limit: 0.075

Calculated Value of PI: 3.1058897382719475

No. of Terms Summed: 28