As the title says, prove each of the following by induction:
a) for every positive integer
b) for all integers
c) is positive for all
d) divides for all positive integers
Show your work, of course.
a) is the propositional function:
Thenb) is the propositional function:
Thenc) is the propositional function:for
since whenHenced) I'll leave this to you. It's rather similar to (c).
Expand and simplify . Then express the resulting expression in the form , and you'll find that is divisible by .
Can you fill in all the gaps?