How Do I Evaluate a Summation Involving Binomial Coefficients?

In summary, summation combinatorics is a branch of mathematics that involves counting and arranging objects using summation notation. The formula for summation combinatorics is nCr = n! / r!(n-r)!, and it has real-life applications in fields like probability and statistics, computer science, and genetics. Common misconceptions about summation combinatorics include its lack of practical use and complexity, but with practice and understanding of the formula, it can be easily applied. Some tips for solving problems in summation combinatorics include clearly defining the problem, understanding restrictions, and using visual aids and practice.
  • #1
mathstime
25
0
how do I evaluate [tex] \sum_{k=0}^d \binom{n+d-k}{n} [/tex] ?
 
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  • #2


I don't know the method. But first you could change the variable of integration to [itex]k'=d-k[/itex] and then you look it up :)
I think the answer is
[tex]\binom{n+d+1}{d}[/tex]
 
  • #3


The answer is:
[tex]\left(
\begin{array}{c}
n+d+1 \\
n+1
\end{array}
\right)[/tex]

Please refer to:

http://www.voofie.com/content/76/evaluating-summation-involving-binomial-coefficients/"

for the steps and how to deal with problem of this type.
 
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What is summation combinatorics?

Summation combinatorics is a branch of mathematics that deals with counting and arranging objects or elements in a specific way. It involves the use of summation notation to represent the total number of possible outcomes in a given scenario.

What is the formula for summation combinatorics?

The formula for summation combinatorics is nCr = n! / r!(n-r)!, where n represents the total number of objects and r represents the number of objects chosen for each combination.

How is summation combinatorics used in real life?

Summation combinatorics has various applications in real life, such as in probability and statistics, where it is used to calculate the number of possible outcomes in a given event. It is also used in computer science for data analysis and in fields like genetics and bioinformatics for analyzing genetic sequences.

What are some common misconceptions about summation combinatorics?

One common misconception about summation combinatorics is that it is only used in theoretical mathematics and has no practical applications. However, as mentioned earlier, it has numerous real-life applications in various fields. Another misconception is that it is a complicated concept, but with practice and understanding of the formula, it can be easily applied to solve problems.

What are some tips for solving problems in summation combinatorics?

Some tips for solving problems in summation combinatorics include clearly defining the problem, understanding the given conditions or restrictions, and making use of visual aids like diagrams or tables to organize the information. It is also helpful to practice solving different types of problems to become familiar with the concept and its applications.

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