Prove that:

1 + 1/2 + 1/3 + ... + 1/n > 2n/n+1

where n>2

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- Jul 26th 2009, 05:11 AMthe undertaker[SOLVED] Prove 1 + 1/2 + 1/3 + ... + 1/n > 2n/n+1
Prove that:

1 + 1/2 + 1/3 + ... + 1/n > 2n/n+1

where n__>__2 - Jul 26th 2009, 05:33 AMred_dog
Prove by induction.

- Jul 26th 2009, 06:00 AMartvandalay11Proof by Induction
This will be a proof by induction

For the base case let n=2.

So which is true so the base case holds

Now we'll assume the statement is true for n and consider it for n+1

Is

(this is an analysis via cross multiplication)

And since 5n>4n for all n, so the statement is proven by induction