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Need help /w a math problem

Originally posted by: Chu
Can anyone tell me what the equality symbol in this problem means?

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Probably means less than or equal to whenever you see that symbol, or greater than or equal to. I think it's just a lazy way of writing concatenating two problems into one.
 
To me it appears like 3 problems. Prove it when using a '>' sign, then prove it when using an '=' sign, and then prove it when using the '<' sign.

I could be wrong though.
 
It's a cases problem. You have to prove the first statement when k takes any of three values... <, =, or >.

Sucks to be you! 😉
 
Yeah, prove it for both 'less than' case, prove it for both 'equal' case and prove it for both 'greater' case
 
I agree, 3 seperate problems. OTOH, what the hell kind of English is "according as?" I would call total shenanigans on the whole problem based merely on that.

Smithers
 
Here is my thoughts on it... Take it as you will:
The rest is trivial...

So if you expand the nCr on both sides you get:
n! / [ (k-1)! * (n-(k-1))! ] ? n!/[k! * (n-k)!]

the numberators are the same so if the denominator is the greater on the left then the value to the right is larger (sign inversion). eg. 1/6 < 1/5

so you have
(k-1)! * (n-(k-1))! ? k! * (n-k)!

substitute
K! = (K-1)! * K on the right side and you have
(k-1)! * (n-(k-1))! ? (K-1)! * K * (n-k)!

Divide through by (k-1)!
(n-(k-1))! ? k * (n-k)!

substitute n-(k-1) = n-k+1
(n-k+1)! ? k * (n-k)!

substitute (n-k+1)! = (n-k)! * (n-k+1)
(n-k)! * (n-k+1) ? k * (n-k)!

divide by (n-k)!
n-k+1 ? k

add k to both sides
n+1 ? 2k

rewritten:
k ? (n+1) / 2

-Smooth
 
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