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(a) Simplify \[\dfrac{\dbinom{n}{k}}{\dbinom{n}{k - 1}}.\] (b) For some positive integer $n,$ the expansion of $(1 + x)^n$ has three consecutive coefficients $a,$ $b,$ $c$ that satisfy $a:b:c = 1:7:35.$ What must $n$ be?

 Jun 8, 2022
 #1
avatar+579 
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Please post one question at a time!!!

 

-Vinculum

 

smileysmileysmiley

 Jun 8, 2022
 #2
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This is A o P S homework.  Do not cheat by posting problems.

 Jun 8, 2022
 #3
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Hey, I don't want to be rude or anything Guest, but you can't just go around assuming something Is an AoPS problem by just looking at it. 

 

At least prove that it is an AoPS problem before going around telling people not to post stuff. 

 

Also please don't say someone is cheating without knowing the full story!

Vinculum  Jun 8, 2022

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