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## Homework Statement

Given a sequence of rational numbers, defined inductively as follows:

s

_{1}= 1, s

_{n+1}= s

_{n}/2 + 1/s

_{n}, n>=1

prove that 1<=s

_{n}<=2 forall n>=1

## Homework Equations

## The Attempt at a Solution

I've got the solution to this but I don't understand a certain part, I was hoping someone could explain it to me?

So Let P(n) be the statement 1<=s

_{n}<=2

P(1) is satisfied.

Suppose P(n) holds.

Then s

_{n+1}= s

_{n}/2 + 1/s

_{n}>= 1/2 + 1/2 = 1, because s

_{n}/2>=1/2 and

**1/s**

_{n}<=1/2The bold part is what i don't understand. Wouldn't that imply that s

_{n}>= 2?

Am I mistaken or is there maybe an error in this solution?

Thanks in advance.