{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Lab3 - Java Programming Lab 3!5 k =1 Question 1 Quick Rule...

This preview shows pages 1–2. Sign up to view the full content.

Java Programming Lab 3 Question 1: Quick Rule for Final Zeros in a Factorial Follow-Up: From our class discussion, the number of final zeros in n ! was seen to be: FZ ( n ) = n 5 k ! " ! # \$ # k = 1 % & where the brackets denote the floor function. The infinite sum can be truncated as soon as 5 k exceeds n , as all the subsequent terms are zero. In Java, the floor function is automatically obtained by computing the division using integers. Here is a modified method that could compute the number of final zeros in n ! for any number up to 1000!. Here are selected results: FZ(100) = 24, FZ(200) = 49, FZ(1000) = 249 Do you notice a pattern? In class we noticed that an approximate answer can be obtained by noting that the number of zeros is strictly less that n /4. In java we can implement this quick rule as: int quickZeros = (n-1)/4; The quick rule follows simply by removing the floor function and using the formula for a geometric series. FZ ( n ) = n 5 k ! " ! # \$ # k = 1 % & < n 5 k k = 1 % & = n 1 5 k – 1 k = 0 % & ( ) * + , - = n 1 1 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern