Combinatrics Problem

  • Thread starter Mithal
  • Start date
  • #1
Mithal
28
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I have this problem as follow

prove that

Summation of k=1 to n to the following term

( (-1)^(k+1) (( 2n-k) C ( k-1)) (4^(n-k))/k ) = ((4^n) - 1)/(2 n +1)

Note that the symbol C above meant the symbol of combination .
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
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14,967
19
I assume you mean:

[tex]
\sum_{k = 1}^{n} (-1)^{k+1} \binom{2n-k}{k-1} \frac{1}{k} 4^{n-k}
= \frac{4^n - 1}{2n + 1}
[/tex]

?

Have you tried anything? Or at least thought about how to begin, even if you weren't able to carry it through?
 
  • #3
Mithal
28
0
Yes , I tried to do it using induction combined with Pascal's identity but it seems it doesn't work . Any suggestions how to go through ?
 

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