Help: sum of binomial coefficents

In summary, the conversation is about finding a closed formula for the sum of the first s binomial coefficients, with s<n. The person asking for help is preparing for an exam and is looking for a trick to derive the formula. However, the responder points out that the sum does not have a closed form and suggests a resource for further reading.
  • #1
thealchemist83
2
0
Help: sum of binomial coefficents !

Hello!
I cannot figure out how to derive a closed formula for the sum of "the first s" binomial coefficients:

[tex]\sum_{k=0}^{s} \left({{n}\atop{k}}\right)[/tex]

with [tex]s<n[/tex]

Could you please help me find out some trick to derive the formula... I've an exam on monday!

Thank you very much!
 
Physics news on Phys.org
  • #2
Oh nevermind, I misread it as the sum of n binomial coefficients.
 
Last edited by a moderator:
  • #3


Dear Thealchemist83,

I have just read your question, long after your exam... If this was your task, I wonder about the mark you've got because this sum does not have a closed form.:smile:

See the fifth chapter of Concrete Mathematics (Graham, Knuth, Patashnik)

Istvan
 

Related to Help: sum of binomial coefficents

What is the "Help: sum of binomial coefficients"?

The "Help: sum of binomial coefficients" is a mathematical concept that involves finding the sum of all the binomial coefficients in a given binomial expansion.

How do you calculate the sum of binomial coefficients?

The sum of binomial coefficients can be calculated using the formula nCr = (n!)/(r!(n-r)!), where n is the total number of terms and r is the specific term being considered.

What is the significance of the sum of binomial coefficients?

The sum of binomial coefficients is important in combinatorics and probability theory as it represents the total number of possible combinations or outcomes in a given situation.

Can the sum of binomial coefficients be simplified?

Yes, the sum of binomial coefficients can be simplified using mathematical identities such as Pascal's triangle or the binomial theorem.

What are some real-world applications of the sum of binomial coefficients?

The sum of binomial coefficients has various applications in fields such as genetics, computer science, and economics. It is used to calculate probabilities, analyze data, and make predictions in these and other areas.

Similar threads

I Probability of White Ball in Box of 120 Balls: Solved!
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
MHB Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
I Randomly Stopped Sums vs the sum of I.I.D. Random Variables
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
I Stuck on the probability of rolling 'p' with 'n' s-sided dice
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
MHB Solve Sum of {30 \choose i} with Binomial Theorem
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
Chernoff Bound for Binomial Distribution
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
A Coefficients of Chebyshev polynomials
    • Linear and Abstract Algebra
Replies
2
Views
1K
Binomial Distribution for successive events
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
2K
Use of binomial theorem in a sum of binomial coefficients?
    • Precalculus Mathematics Homework Help
Replies
1
Views
1K
What is the closed form for the sum of binomial coefficients over any interval?
    • Calculus
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top