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 hour ago Russia Invades Ukraine View the latest post Replies 643 Views 209050
- by Eli 1 hour ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 30 Views 42686
- by Eli 5 hours ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 273 Views 6497
- by Eli 1 day ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 21 Views 22654
- by Eli 5 days ago Re: What is in Your Mind? View the latest post Replies 658 Views 271345
- by Eli 6 days ago Mission Control Live: NASA InSight Mars Landing Live Coverage View the latest post Replies 32 Views 12958
- by Eli 6 days ago Christian Podcasts View the latest post Replies 4 Views 28279
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 7 Views 2713
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 32 Views 44704
- by Eli 2 weeks ago C++ PROGRAMMING CRASH COURSE View the latest post Replies 4 Views 1289
-
Groups: Proof by Induction - Solved example
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests