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## Homework Statement

Let ##x,y## be positive numbers. Let ##a_0 = y## and let ##a_n = \frac{(x/a_{n-1})+a_{n-1}}{2}##. Prove that ##(a_n)## is a decreasing sequence with limit ##\sqrt{x}##.

## Homework Equations

## The Attempt at a Solution

I'm confused about the initial condition being an arbitrary positive real number. This is because it says to prove that ##(a_n)## is a decreasing sequence, but what if ##0<y< \sqrt{x}##? Then ##(a_n)## can't be decreasing...