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**buenogilabert** Hi, I have the following problem which I don't know how to solve... I know how to do part C, but I don't know parts A and B. I will have enough to guide myself if you help me with part A though.

Thanks a lot!

The whole problem is:

"Let $\displaystyle f(x)=(x^2+3)/(2x)$ for $\displaystyle x \not= 0$. Define a sequence of real numbers $\displaystyle x_n$ by

$\displaystyle x_{n+1} =f(x_n)$ for $\displaystyle n \geq 1$, $\displaystyle x_1=2$.

A) Show that if $\displaystyle x> \sqrt 3$, then $\displaystyle f(x)> \sqrt 3$.

B) Show that if $\displaystyle x> \sqrt 3$, then $\displaystyle x>f(x)$. (Hint: show $\displaystyle x-f(x)>0$.)

C) Conclude that the sequence $\displaystyle x_n$ converges."