The induction question is. for all natural n, n4 <= 4n + 17
Base case: 0 Works, since 0 < 1 + 17 then,
I assume that for all n in natural, n4 <= 4n + 17 holds.
Now I believe I need to show that, 4(n4) <= 4(4n + 17)
that is, 4n+1 + 17 >= (n+1)4
To do so, I prove, 4n4 >= (n+1)4,
which proves that 4n+1 + 17 >= (n+1)4
How would I prove.. 4n4 >= (n+1)4 = n4 + 4n3 + 6n2 + 4n + 1
This step is in the middle of my induction proof and it is neccesary part of my induction step.
How would I go about doing this?
Some easier version similar to this deals with power of 2 or n, which seems rather simple. but, this one I am having hard time.
Help is much appreciated.
The Attempt at a Solution
I tried starting from n4 = n4 and start adding things to both sides but the onlything I can add to left is n4 so I am not entirely sure how to go about doing this type of math. please some tricks and help is appreciated.