Proof by induction inequality

Prove for all

__Proof__: i) Show P(1) holds.

LHS =

RHS =

LHS RHS, thus, P(1) holds.

ii) Assume P(k) holds for some

That is, assume .

To show: P(k + 1):

Then

Not sure what to do next. In my next step, I said . But I'm not sure if this is the right path to take.

Re: Proof by induction inequality

Quote:

Originally Posted by

**deezy** Prove

for all

__Proof__: i) Show P(1) holds.

LHS =

RHS =

LHS

RHS, thus, P(1) holds.

ii) Assume P(k) holds for some

That is, assume

.

To show: P(k + 1):

Then

Not sure what to do next. In my next step, I said

. But I'm not sure if this is the right path to take.

What you have done is fine, but you need to state why that inequality is true, the reason being that for all . Then you can say .

Re: Proof by induction inequality

But I'm not sure how I can use since it isn't less than .

Re: Proof by induction inequality

Now you just have to prove that is greater than or equal to ,

because that would give you the result .

But needed inequality holds since

.