Some practice problems that I am stuck on, in my first week of this class.
Prove that 1^3+2^3...+n^3 = (1+2+...n)^2
Prove that 11^n+1 + 12^n+1 is divisible by 133
I can only show that these are true by using examples (i.e plugging stuff in). I don't know how to do the proof for either one.
so for the first one I would prove that the statement is true for 1 to 2 (minimum set/basis case) then prove that it if its true for some n (that i don't need to specify), that it must be true for n+1?
for the second one i would probe that its true for n=1, and then what? prove that if its true for some n, that it must be true for n+1 again? or something else?
I will do these quickly and show you if that's ok, I want to make sure I understand this correctly.
thanks
EDITED