Difference between revisions of "Manuals/calci/LUCAS"
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| − | <div style="font-size:30px">'''LUCAS( | + | <div style="font-size:30px">'''LUCAS (NumberUpto)'''</div><br/> |
| − | *<math> | + | *<math>NumberUpto</math> is the number indicating the position. |
| + | **LUCAS(),returns the sum of its two immediate previous terms. | ||
==Description== | ==Description== | ||
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*Lucas numbers are similar to the Fibonacci numbers. | *Lucas numbers are similar to the Fibonacci numbers. | ||
*It is generated by added the last two numbers in the series. | *It is generated by added the last two numbers in the series. | ||
| − | *In <math>LUCAS( | + | *In <math>LUCAS(NumberUpto)</math>, <math>NumberUpto</math> 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 <math>L_0=2</math> and <math>L_1=1 </math>, but <math>F_0=0</math> and <math>F_1=1</math>. | *The difference between Lucas and Fibonacci numbers are with the first two terms <math>L_0=2</math> and <math>L_1=1 </math>, but <math>F_0=0</math> and <math>F_1=1</math>. | ||
*The Lucas numbers are defined by: | *The Lucas numbers are defined by: | ||
| − | <math>L_n=\begin{ | + | <math>L_n=\begin{Bmatrix} 2 & if & n=0 \\ |
| − | 1 &if | + | 1 &if & n=1 \\ |
| − | L_{n-1}+L_{n-2} &if | + | L_{n-1}+L_{n-2} &if & n>1 |
| − | \end{ | + | \end{Bmatrix}</math> |
*The sequence of Lucas numbers is 2,1,3,4,7,11,18,29.... | *The sequence of Lucas numbers is 2,1,3,4,7,11,18,29.... | ||
*The relation between Lucas and Fibonacci numbers are: | *The relation between Lucas and Fibonacci numbers are: | ||
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<math> F_n=\frac{L_{n-1}+L_{n+1}}{5}</math> | <math> F_n=\frac{L_{n-1}+L_{n+1}}{5}</math> | ||
where <math>L</math> is the Lucas series with <math> L_n</math> is the <math>n^{th}</math> Lucas number and <math> F_n </math> is the <math>n^{th}</math> Fibonacci number. | where <math>L</math> is the Lucas series with <math> L_n</math> is the <math>n^{th}</math> Lucas number and <math> F_n </math> is the <math>n^{th}</math> Fibonacci number. | ||
| − | This function will, give the result as error when <math> | + | This function will, give the result as error when <math>NumberUpto</math> is non-numeric or NumberUpto < 0 |
==Examples== | ==Examples== | ||
Latest revision as of 16:26, 25 June 2018
LUCAS (NumberUpto)
- is the number indicating the position.
- LUCAS(),returns the sum of its two immediate previous terms.
is the number indicating the position.
Description
- This function gives the Lucas series of the numbers.
- Lucas numbers are similar to the Fibonacci numbers.
- It is generated by added the last two numbers in the series.
- In , 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 and , but and .
- The Lucas numbers are defined by:
, 
and 
, but 
and 
.
- The sequence of Lucas numbers is 2,1,3,4,7,11,18,29....
- The relation between Lucas and Fibonacci numbers are:
and : where is the Lucas series with is the Lucas number and is the Fibonacci number.
and :
where 
is the Lucas series with 
is the 
Lucas number and 
is the This function will, give the result as error when is non-numeric or NumberUpto < 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
Related Videos
See Also
References