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# Proof by induction watch

1. 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.

2. Ok, we assume that for some integer k. We need to show that this (implies) that

Spoiler:
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3. 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.
4. Divide out the fraction, and then if un > 5, what's the restriction on un+1

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Updated: January 29, 2009
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