Binomial Theorem

  • Thread starter EngWiPy
  • Start date
  • #1
1,367
61
Hello,

All we know the Binomial Theorm which may be stated mathematically as:

[tex]\left(x+y\right)^n=\sum_{k=0}^n{n\choose k}y^k\,x^{n-k}[/tex]

Now suppose that we have the following mathematical expression:

[tex]\sum_{k=0}^{n}{n\choose k}\,(-1)^k[/tex]

if we substitute x=1 and y=-1 in the first equation we get the second. Is that mean the second equation is essentially zero, since [tex](1-1)^n=0[/tex]??

Regards
 

Answers and Replies

  • #2
367
1
Yes, indeed, unless n = 0.
 
  • #3
1,367
61
Yes, indeed, unless n = 0.

Why? In the case that n = 0, what will be the answer? 1?
 
  • #4
1,015
70
00 is not well-defined and neither is 0Ck for any k <> 0 (although there are generalizations that extend the domain beyond the definition using just factorials).
 

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