Difference between revisions of "Manuals/calci/ARITHMETICSERIES"

Revision as of 15:18, 22 September 2016

ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)

This function gives the Arithmetic series of the numbers.
An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d.
Therefore, for k>1,

 $a_{k}=a_{(k-1)}+d=a_{(k-2)}+2d=...=a_{1}+d(k-1)$ .

$S_{n}=sum_{(k=1)}^{(n)}a_{k}$

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-<div style="font-size:30px">'''ANGLE (deg,by,till)'''</div><br/>
+<div style="font-size:30px">'''ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)'''</div><br/>
-*<math>deg</math> is the starting angle value in degree
+*<math>Start</math> is the starting  value
-*<math> by </math> is the skip value.
+*<math> Difference </math> is the difference value of the series.
+*<math>Numbers</math> is the positive real number.
+==Description==
+*This function gives the Arithmetic series of the numbers.
+*An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant  d.
+*Therefore, for k>1,
+ <math>a_{k}=a_{(k-1)}+d=a_{(k-2)}+2d=...=a_{1}+d(k-1)</math>.
+*The sum of the sequence of the first n terms is then given by
+<math>S_{n} = sum_{(k=1)}^{(n)}a_{k}</math>