Forgot to mention, both b and a are positive integers.
I just can't figure this out. Can someone point me in the right direction? I need to prove, that for all b >= a:
Two hints I was given were (first one is possible because b > a):
and
I've tried everything I could think of...using the binomial formula, expanding the first hint, etc. Always seem to hit dead ends.
The first hint implies that it's enough to show that (*) .
By direct calculation, , where the last inequality holds because . For convenience we refer only to the sum inside the brackets.
Now it follows by the Binomial Theorem that , where for the last inequality I applied the second hint.
Therefore, and from (*) the result follows.