Given any real number and positive integer , prove that

Deduce that for any real number and positive integers and , one has

I think the second part is very straightforward i.e.

I just can't prove the initial part.

Any help appreciated!

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- Apr 12th 2012, 09:05 AMleshieldsFloor functions!
Given any real number and positive integer , prove that

Deduce that for any real number and positive integers and , one has

I think the second part is very straightforward i.e.

I just can't prove the initial part.

Any help appreciated! - Apr 12th 2012, 10:07 AMa tutorRe: Floor functions!
Let where and and q and r are integers.

I think this goes somewhere. - Apr 13th 2012, 11:27 AMleshieldsRe: Floor functions!
Cheers, think I get it.. So by putting as you suggest we have and as so

Now as and , and we have so also.

Therefore