Mathematical induction exercises

2)

a)

Base step



Induction step

Replacing proven part by

b)

Base step



Induction step

#todo finish the induction step

4)

#todo Prove that the problem works for n = 1
#todo The next square can be constructed out of 4 previous squares and a n=1 square

5)

Base step



Induction step

Strong induction

1)

Base steps






Induction step



Short explanation

We calculate the numbers for the 5 cases proceeding 24 (itself included)
We go back 5 cases from the case and since that falls into our range (beacause ) we know that the values of a and b exist.
Therefore we can go back to our case adding 5 to the case by substituting for

4)Fibonacci





Induction step

Dividing everything by