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    I have come across this proof, and hav no idea how to do it.

    Q. The sequence of real numbers U1,U2, U3,... is such that U1=5.2 and Un+1=(6un+10)/(un+3).

    Prove by induction that Un>5, for all positive integers.

    Please help, i can do the basis but do not know what to assume or induct.
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    Ok, we assume that U_k > 5 for some integer k. We need to show that this \Rightarrow (implies) that U_{k+1} >5

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    \displaystyle \frac{6x+10}{x+3} = 6 - \frac{8}{x+3}
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    Prove for n=1 (trivial since 5.1 > 5). Then assume for n=k that U[k] > 5 with your aim to prove for U[k+1] > 5.

    If you get stuck, post back with a little working.
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    Divide out the fraction, and then if un > 5, what's the restriction on un+1
 
 
 
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