- #1
googlymunja32
- 4
- 0
kx = x !/r! (x – r)! kx− r
is that right?
is that right?
Binomial theorum, when k is a multiple of x
In summary, the binomial theorem is a mathematical formula used to expand expressions of the form (a + b)^n, where n is a positive integer. K in the binomial theorem refers to the number of times the variable x appears in the expression. When k is a multiple of x, it means that k is divisible by x without leaving a remainder and x is a factor of k. The binomial coefficient can be calculated using the formula (n choose k/x) when k is a multiple of x, and (n choose k) when k is not a multiple of x. The binomial theorem can still be applied in both cases.
- #2
mathman
Science Advisor
- 8,140
- 572
googlymunja32 said:
The right side of your equation is confusing. Put in some parentheses.
- #3
- #4
mathman
Science Advisor
- 8,140
- 572
The thunbnail is hard to read. In the second equation there are terms with k to some exponent. It is hard to read these exponents. Also, what is the question - prove the second equation holds?
1. What is the binomial theorem?
The binomial theorem is a mathematical formula used to expand expressions of the form (a + b)^n, where n is a positive integer. It allows us to find the coefficients of each term in the expansion.
2. What is k in the binomial theorem?
K in the binomial theorem refers to the number of times the variable x appears in the expression. It is also known as the degree of the binomial and is represented as n in the formula (a + b)^n.
3. What does it mean when k is a multiple of x?
When k is a multiple of x, it means that k is divisible by x without leaving a remainder. In other words, x is a factor of k. This is important in the binomial theorem as it affects the coefficients of the terms in the expansion.
4. How do you calculate the binomial coefficient when k is a multiple of x?
When k is a multiple of x, the binomial coefficient can be calculated using the formula (n choose k/x), where n is the degree of the binomial and k/x is the number of times x appears in the expansion. This can also be simplified as (n choose k/x) = (n choose k).
5. Can the binomial theorem be applied when k is not a multiple of x?
Yes, the binomial theorem can still be applied when k is not a multiple of x. In this case, the binomial coefficient can be calculated using the formula (n choose k), where n is the degree of the binomial and k is the number of times x appears in the expansion.
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