Prove by induction :
2n + 1 <= 2^n for n = 3, 4, . . .
I understand the concept of induction, you prove P(0), which in this case is 2(3) +1 <= 2 ^ 3 which is 7 < = 8 which is true, then you assume n = k and try to use that to prove n = (k + 1)
However I always have trouble doing the final induction step. I've been looking at examples online, but I can't follow them because they show most of the steps but don't explain them, so I have trouble understanding exactly what they're doing and why. If anyone can show me how to do the final induction proof and explain each step I'd be really grateful, thanks!
2n + 1 <= 2^n for n = 3, 4, . . .
I understand the concept of induction, you prove P(0), which in this case is 2(3) +1 <= 2 ^ 3 which is 7 < = 8 which is true, then you assume n = k and try to use that to prove n = (k + 1)
However I always have trouble doing the final induction step. I've been looking at examples online, but I can't follow them because they show most of the steps but don't explain them, so I have trouble understanding exactly what they're doing and why. If anyone can show me how to do the final induction proof and explain each step I'd be really grateful, thanks!
