I need to prove by induction on n, that
4^1 + 4^2 + 4^3 +....+ 4^n = 4/3 (4^n) - 1
For all integers 'n' is = or > than 1
Thank you very much!
a) check the initial case: here, you have to check the identity when .
b) perform the induction step: assume that, for some , ; then you have to prove that (same identity with instead of ). To do this, simply note that (using the assumption), and after simplification you should get what you need. This will conclude the induction.