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 23 hours ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 324 Views 28688
- by Eli 1 day ago Re: What is in Your Mind? View the latest post Replies 700 Views 294154
- by Eli 3 days ago Russia Invades Ukraine View the latest post Replies 661 Views 229801
- by Eli 4 days ago President Museveni's Speech During International Development Association (IDA) Summit View the latest post Replies 1 Views 212
- by Eli 4 days ago From Simple Linear Regression Analysis to Covariance & Correlation to Independent Determinant, and R-Squared View the latest post Replies 11 Views 24488
- by Eli 1 week ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 62256
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 57761
- by Eli 1 week ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 11144
- by Eli 2 weeks ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 10966
- by Eli 2 weeks ago Python Packages for Scientific Computing View the latest post Replies 8 Views 17338
-
Groups: Proof by Induction - Solved example
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests