Binomial problem (1 Viewer)

[followme]

I need help with this question:​

​

The coefficient of x<SUP>k</SUP> in (1 + x)<SUP>n</SUP>, where n is a positive integer, is denoted by<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>​

C<SUB>k</SUB> (so C<SUB>k</SUB> = <SUP>n</SUP>C<SUB>k</SUB>)<o></o>​

Show that<o></o>​

C<SUB>0</SUB>+<?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-comffice:smarttags" /><st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="False" SourceValue="2" UnitName="C">2C</st1:chmetcnv><SUB>1</SUB>+<st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="False" SourceValue="3" UnitName="C">3C</st1:chmetcnv><SUB>2</SUB>+…+(n+1)C<SUB>n</SUB> = (n+2)2<SUP>n-1</SUP>​

<SUP></SUP><o></o>​

Thanks for any help.

 

[followme]

wow, it works perfectly, thanx a lot! I think by expanding (1+x)^n and substitute x=1, would be easier to prove []=2^n

btw, which topic is "Gauss method" from? I don't seem to remember ...

 

[Riviet]

btw, which topic is "Gauss method" from? I don't seem to remember ...

I believe Gauss is not specifically mentioned in the syllabus, but this topic is obviously the binomial theorem.