Manuals/calci/LUCAS
LUCAS(n)
- 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 the number indicating the position.
Description
- This function gives the Lucas series of the numbers.
- Lucas numbers are similar to the Fibonacci numberss.
- It is generated by added the last two numbers in the series.
- 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 LUCAS(n), n } is the numbers position, which is used to displaying the numbers in the given range.
- The difference between Lucas and Fibonacci numbers are with the first two terms 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 L_0=2} 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 L_1=1 } , but Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle F_{0}=0} 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 F_1=1} .
- The Lucas numbers are defined 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 L_n=\begin{cases} 2 if n=0 \\ 1 if n=1 \\ L_{n-1}+L_{n-2} if n>1 \end{cases}}
- The sequence of Lucas numbers is 2,1,3,4,7, 11,18,29,......
- The relation between Lucas and Fibonacci numbers are: 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 L_n=F_n+2F_{n-1} } 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 F_n=\frac{L_{n-1}+L_{n+1}}{5}}
where L is the Lucas series with 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 L_n} is the nth Lucas number 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 F_n } is the nth Fibonacci number.
This function will give the result as error when n is nonnumeric or n < 0
Examples
- =LUCAS(5)= 2 1 3 4 7 11
- =LUCAS(0)= 2
- =LUCAS(1)= 2 1
- =LUCAS(3)= 2 1 3 4
- =LUCAS(-1)=Null