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What is the relationship between Pascal triangle and binomial theorem?
The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.
What is the comparison between pascal triangle expansion and binominal expansion?
Pascal's triangle shows the constant for each term if the equation is (x+y) to a number, which is the line number in Pascal's triangle, for a binomial expansion you can use Pascal's triangle but you have to multiply that by the constants on x and y raised to x's and y's exponent multiplied by the number the binomial is being raised to. (ax^b + cy^d) ^e = the number in Pascal's triangle for e times (a^ (b times e)) times (c ^(d times e)) which gives the constant for that term
What is the significance of Pascal's triangle?
It generates binomial coefficients.
What is another name for pascals triangle?
The expanded binomial is another name for Pascal's triangle.
What did Blaise Pascal invent?
Blaise Pascal (France, 1623-1662) His inventions include the hydraulic press and the syringe.Hope this helps!Pascal was a mathematician in the 17th century. He described Pascal's Triangle, possibly one of the easiest methods of binomial expansion.
What is the relationship between Pascal triangle and binomial theorem?
The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.
Discovered Pascal's triangle and binomial expansion before Pascal?
blaise pascal didn't discover Pascal's Triangle the Persians and Chinese discovered it.
What are the applications of pascal's triangle?
For binomial expansions. (When you have to multiply out many brackets, binomial expansion speeds things up greatly).
What is the comparison between pascal triangle expansion and binominal expansion?
Pascal's triangle shows the constant for each term if the equation is (x+y) to a number, which is the line number in Pascal's triangle, for a binomial expansion you can use Pascal's triangle but you have to multiply that by the constants on x and y raised to x's and y's exponent multiplied by the number the binomial is being raised to. (ax^b + cy^d) ^e = the number in Pascal's triangle for e times (a^ (b times e)) times (c ^(d times e)) which gives the constant for that term
What is the significance of Pascal's triangle?
It generates binomial coefficients.
What is another name for pascals triangle?
The expanded binomial is another name for Pascal's triangle.
What did Blaise Pascal invent?
Blaise Pascal (France, 1623-1662) His inventions include the hydraulic press and the syringe.Hope this helps!Pascal was a mathematician in the 17th century. He described Pascal's Triangle, possibly one of the easiest methods of binomial expansion.
What triangle was Blaise Pascal credited for?
Pascal continued to influence mathematics throughout his life. His Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") of 1653 described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle.
What is Binomial Expansion and how does it relate to Pascal's Triangle?
The binomial expansion is the expanded form of the algebraic expression of the form (a + b)^n.There are slightly different versions of Pascal's triangle, but assuming the first row is "1 1", then for positive integer values of n, the expansion of (a+b)^n uses the nth row of Pascals triangle. If the terms in the nth row are p1, p2, p3, ... p(n+1) then the binomial expansion isp1*a^n + p2*a^(n-1)*b + p3*a^(n-2)*b^2 + ... + pr*a^(n+1-r)*b^(r-1) + ... + pn*a*b^(n-1) + p(n+1)*b^n
What is the purpose of Pascal's triangle?
The Pascal's triangle is used partly to determine the coefficients of a binomial expression. It is also used to find the number of combinations taken n at a time of m things .
Omar Khayyam the Persian philosopher and mathematician created the triangle identical to Pascal's triangle I wonder if anyone is aware of that?
Yes, Omar Khayyam, a renowned Persian philosopher and mathematician from the 11th century, developed a form of what is now known as Pascal's triangle, which he used in his work on binomial coefficients. His triangle, often referred to as Khayyam's triangle, systematically arranged numbers that represent the coefficients in the expansion of binomials. This concept, although not as widely recognized as Pascal's triangle, highlights the historical contributions of Middle Eastern scholars to mathematics long before Pascal's time in the 17th century.
What are some cool fact on pascals triangle?
Pascal's triangle is a triangular array where each number is the sum of the two numbers above it. The numbers in the triangle have many interesting patterns and relationships, such as the Fibonacci sequence appearing diagonally. Additionally, the coefficients of the binomial expansion can be found in Pascal's triangle, making it a useful tool in combinatorics and probability.
