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AlbertEinstein
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Is it always necessary that C(n,r) is an integer if n and r are integers ?
Is there any proof ?Please clarify.
thanks.
Is there any proof ?Please clarify.
thanks.
AlbertEinstein said:If the above statement is trivial, does the following theorem requires a proof:
Th: Prove that p divides C(mp,r) where p is a prime and r is an integer not divisible by p.
AlbertEinstein said:Hey playdo,I understood only the first paragraph.I showed that C(mp,r) is a multiple of p and hence the theorem follows.Does my proof lack something? I didn't understand what Div is .Could you explain in some more basic terms?
Thanks.
The coefficient of binomial expansion refers to the numerical value that appears in front of the variables in a binomial expression when it is expanded. It is calculated using the binomial coefficient formula, which takes into account the number of terms, the power of each term, and the order of the expansion.
The coefficient of binomial expansion is calculated using the binomial coefficient formula, which is nCr, where n is the total number of terms and r is the power of the term being evaluated. This formula can also be written as n! / (r! * (n-r)!), where ! represents the factorial function.
The coefficient of binomial expansion is significant because it represents the number of ways a specific term can be obtained when a binomial expression is expanded. It also helps in simplifying complicated calculations and identifying patterns in the expansion.
No, the coefficient of binomial expansion cannot be negative. This is because the binomial coefficient formula takes into account the number of ways a term can be obtained, which is always a positive value. However, the term itself may be negative depending on the expression being expanded.
The coefficient of binomial expansion is used in various fields such as statistics, probability, and computer science. It is used to calculate the probability of certain events, analyze data, and simplify complicated mathematical expressions. It is also used in computer algorithms, specifically in combinatorial problems and in generating random numbers.