• Support PF! Buy your school textbooks, materials and every day products Here!

Combinatorics Class - Sum Question

  • Thread starter theRukus
  • Start date
  • #1
49
0

Homework Statement


For any positive integer n determine:

[itex]\sum\limits^n_{i=0} \frac{1}{i!(n-i)!}[/itex]


Homework Equations



I don't really know where to start.. Up until this point we've just been doing permutations, combinations, and determining the coefficient of a certain term in the expansion of a polynomial. There aren't any examples like this question in the text, and so I am unsure as to what sort of an answer they are looking for... Are they just looking for a general formula (not a sum) for the answer, with n as a variable? Cheers for any direction!!


The Attempt at a Solution

 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
180
Hint: does this look familiar?

[tex]\frac{n!}{i!(n-i)!}[/tex]
 
  • #3
49
0
So the answer I'm looking for is

[itex]\frac{\dbinom{n}{i}}{n!}[/itex]

Correct?
 
  • #4
49
0
Or will it be

[itex]\sum\limits^n_{i=0} \dfrac{\dbinom{n}{i}}{n!}[/itex]

I'm confused as to whether the sum is still involved.
 
  • #5
54
0
you should find the following sum:

[itex] \frac{1}{n!}*\sum \frac{n!}{i! (n-1)!} [/itex]
 
  • #6
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
Or will it be

[itex]\sum\limits^n_{i=0} \dfrac{\dbinom{n}{i}}{n!}[/itex]

I'm confused as to whether the sum is still involved.
Of course the sum is still involved. The final answer must be in terms of n alone: it cannot contain "i", since all values of i have been summed over. Anyway, just multiplying and dividing by n! does not magically get rid of the sum.

RGV
 

Related Threads on Combinatorics Class - Sum Question

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
18
Views
5K
  • Last Post
Replies
2
Views
695
  • Last Post
Replies
2
Views
918
  • Last Post
Replies
2
Views
841
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
Top