01204211/activity3 induction 1
- This is part of 01204211-58
In-class activities 3
A.1 (LPV) Prove that for any integer , we have that
In problem A.1, you have to state clearly the property that you want to prove. Note that we use variable in the statement, to avoid confusion, you should choose other variables when you work on the inductive step.
A.2 (MN) Prove that for any integer , the following formula is true:
In problem A.2, you have to state clearly the property that you want to prove.
A.3 (MN-exercise-1b) Prove that for integer ,
A.4 (MN-exercise-3a) Draw lines in the plane in such a way that no two are parallel and no three intersect in a common point. How many parts do the lines divide the plane into? Experiment, guess the value, and prove it by induction.
Homework 3
- Due: 16 Sept 2015
H.1 (LPV-2.1.5) Prove the following identity:
H.2 (LPV-2.5.4b) Prove that for any integer , is a multiple of 6.