Math Is Fun Forum

dchilow

Member

Registered: 2007-03-05

Posts: 27

Induction proof help!

Prove that  m^2 - 25m > 0     for all m>25

Proof by induction:
Basic step:
Assume P(m): m^2 - 25m > 0  for all m>25
Prove P(m+1): (m+1)^2 - 25(m+1) > 0

Induction step:  P(m+1):  (m+1)^2 - 25(m+1)= m^2 - 25m + 2m - 24  This is where I am stuck!  I don't know what to do from here.

Could someone please help?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Induction proof help!

First, don’t forget to show that the statement is true for the first value, in this case m = 26. Although it doesn’t matter whether this is done before or after the inductive step, people tend to forget it if they leave it till later; therefore it is good commonsense practice to make a habit of doing this before the inductive step.

For the inductive step, you have

You know that m[sup]2[/sup]−25m > 0 by the inductive hypothesis; for the other half,

Hence

.

dchilow

Member

Registered: 2007-03-05

Posts: 27

Re: Induction proof help!

Thank you so much this was a great help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Induction proof help!

Hi;

Or you could try:

Which is clearly true for m>25.

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