Here are the problems. They will teach you how to prove mathematical statements by using induction method.
Problem 1
Let such that , for a fixed integer . Prove that positive, .
Proof
For , (true)
Let , we need to show that
So,
Suppose it is true for , i.e., , we show that it is also true for
Thus, , hence shown.
Problem 2
Let be a group and suppose that . Show that for any positive integer
Proof
The statement for is simply which is certainly true.
For
Hence the result is true for
Now, assume that the result holds for
Using this induction hypothesis, we have
The statement holds for so by induction it holds for all values of
-
- Active Topics
-
-
- by Eli 1 day ago Re: What is in Your Mind? View the latest post Replies 697 Views 288124
- by Eli 1 day ago Russia Invades Ukraine View the latest post Replies 655 Views 223918
- by Eli 2 days ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 56931
- by Eli 3 days ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 57570
- by Eli 4 days ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 6012
- by Eli 1 week ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 5523
- by Eli 1 week ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 319 Views 23025
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 8 Views 12189
- by Eli 1 week ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 3028
- by Eli 3 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 4726
-
Groups: Proof by Induction - Solved example
-
- Information
-
Who is online
Users browsing this forum: No registered users and 1 guest