You made a simple sign mistake somewhere, it seems.talolard said:Homework Statement
Calculate [tex] \sqrt{1/20} [/tex] using the extended binomial theormem. (a precision of k=4 is enough)
The Attempt at a Solution
[tex] \sqrt{1/20}= (1 + (-19/20) )^{1/2}= \sum( choose (1/2,k)*(-19/20)^k) = 1- 1/2*19/20-1/8*361/400+1/16*6589/8000 = 0.72... [/tex] is wrong.
Homework Statement
Where is my mistake?
Thanks
Tal
The extended binomial theorem is a mathematical theorem that expands the binomial expression (a + b)^n, where n is a positive integer, to include terms with fractional and negative exponents.
The formula for the extended binomial theorem is (a + b)^n = Σ(nCr)(a^(n-r))(b^r), where nCr represents the combination of n items taken r at a time, and a and b are constants.
The extended binomial theorem is derived using the binomial theorem and the concept of a general term in a binomial expansion. By expanding (a + b)^n using the binomial theorem and then manipulating the terms to include fractional and negative exponents, the extended binomial theorem is obtained.
The extended binomial theorem has various applications in mathematics, physics, and engineering. It is used to solve problems involving probability, series and sequences, and to expand trigonometric functions. It can also be applied in calculus to evaluate limits and to find derivatives and integrals.
Yes, there are limitations to the extended binomial theorem. It can only be applied to binomial expressions, where there are two terms being raised to a power. It also assumes that the exponents in the expanded terms are real numbers, so it cannot be used for complex numbers. Additionally, the extended binomial theorem is only accurate when the power (n) is a positive integer.