Find out if this statement is true or false. If true, provide a proof. If false, provide a counterexample?

Question

For nЄN,

[2n-18]/[(n^2)-8n+8] < 1

I think this has to be done with induction? I'm not sure how to do it though. Could someone help?

Answer 1

it is false at n=2

(2*2-18)/(2^2 - 8*2 + 8)
= (4-18)/(4-16+8)
= -14 / -4
= 7/2 > 1

Answer 2

Even if it were true, you probably wouldn't prove it by induction. You'd just look at the function defined by the left hand side defined over the range, say, [1, infinity), and as a last step check whether restricting the range to the natural numbers made any difference.

Answer 3

i'm assuming that R denotes the set of all real numbers. it rather is particularly ordinary to make a counterexample. The function f(x) = x is non-provide up, via fact that all polynomial purposes are non-provide up, yet this function is obviously unbounded on R. So the fact is fake.