Manuals/calci/BINOMIALSERIES
BINOMIALSERIES (N,X,Y)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_1,n_2,n_3...} are any real numbers.
Description
- This function gives the coefficient of the Binomial series.
- BinomialSeries is also called Maclaurin series for the function f given by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=(1+x)^{\alpha}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is belongs to any Complex number.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BINOMIALSERIES(N,X,Y)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is any positive integer and x and y are any real numbers.
- If k is any number and |x|<1 then,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1+x)^k= \sum_{n=0}^\infty \binom{k}{n} x^n} whereFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \binom{k}{n} = \frac{k(k-1)(k-2)...(k-n+1)}{n!} } ,n=1,2,3...http://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx.
- So similar to the binomial theorem except that it’s an infinite series and we must have in order to get convergence.
- This function will give the result as error when
- 1. N is not positive number.
- 2. N,X and Y is a Non-numeric.