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The Binomial Theorem states that for any non-negative integer ( n ) and any real numbers ( x ) and ( y ):
[ (x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k ]
where ( \binom{n}{k} = \frac{n!}{k!(n-k)!} ) is the binomial coefficient. The proof can be done using mathematical induction on ( n ). For the base case ( n=0 ), ( (x+y)^0 = 1 ) matches the theorem. Assuming it holds for ( n ), for ( n+1 ), we can write ( (x+y)^{n+1} = (x+y)(x+y)^n ) and expand using the induction hypothesis, leading to the correct form of the theorem after simplification.
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Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
Who created the binomial theorem?
The binomial theorem is attributed to several mathematicians throughout history, but it was most notably developed by Isaac Newton in the late 17th century. While the formula for expanding powers of a binomial expression had been known in simpler forms before him, Newton generalized it for any positive integer exponent. The theorem expresses the expansion of ((a + b)^n) as a sum involving binomial coefficients.
What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
What is the relationship between probability and the binomial theorem?
What is the symbol for a Probability of success in a binomial trial?
Who invented binomial theorem?
AnswerThe binomial theorem has been known for thousands of years. It may have first been discovered in India around 500 BC.
Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
Who created the binomial theorem?
The binomial theorem is attributed to several mathematicians throughout history, but it was most notably developed by Isaac Newton in the late 17th century. While the formula for expanding powers of a binomial expression had been known in simpler forms before him, Newton generalized it for any positive integer exponent. The theorem expresses the expansion of ((a + b)^n) as a sum involving binomial coefficients.
What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
Did Isaac newton co create the binomial theorem?
yes Isaac Newton created the binomial theorem
How do you use binomial theorem in daily life?
You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".
How did Sir Isaac Newton contribute to algebra?
Binomial expansions and the binomial theorem,\.
What is the meaning binomial?
A binomial is a polynomial with two terms. It is an algebraic expression consisting of two terms connected by either addition or subtraction. It is commonly seen in the form of (a + b)^n in binomial theorem, where a and b are variables and n is a non-negative integer.
How can we use of binomial theorem in pharmacy?
Binomial Theorem consists of formulas to determine variables. In pharmacy it can be used to calculate risks and costs of certain medications.
What is the relationship between probability and the binomial theorem?
What is the symbol for a Probability of success in a binomial trial?
Who invented binomial theorem?
AnswerThe binomial theorem has been known for thousands of years. It may have first been discovered in India around 500 BC.
How do you solve 5.4e0.06t using the fundamental theorem of calculus?
We need more information. Is there a limit or integral? The theorem states that the deivitive of an integral of a function is the function
Why is the binomial theorem important for daily life?
suck my balls
