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## Homework Statement

The induction question is. for all natural n, n

^{4}<= 4

^{n}+ 17

Base case: 0 Works, since 0 < 1 + 17 then,

I assume that for all n in natural, n

^{4}<= 4

^{n}+ 17 holds.

Now I believe I need to show that, 4(n

^{4}) <= 4(4

^{n}+ 17)

that is, 4

^{n+1}+ 17 >= (n+1)

^{4}

To do so, I prove, 4n

^{4}>= (n+1)

^{4},

which proves that 4

^{n+1}+ 17 >= (n+1)

^{4}

How would I prove.. 4n

^{4}>= (n+1)

^{4}= n

^{4}+ 4n

^{3}+ 6n

^{2}+ 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.

## Homework Equations

## The Attempt at a Solution

I tried starting from n

^{4}= n

^{4}and start adding things to both sides but the onlything I can add to left is n

^{4}so I am not entirely sure how to go about doing this type of math. please some tricks and help is appreciated.

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