Arithmetic sequences and series

 A Sequence is the list of numbers written in a particular order following a pattern. A Series is the sum of the list of the numbers written in the specific order in a sequence. The sequence and series can have numbers extending up till infinity and they are called infinite sequence and infinite series.

General Sequence:

Example:

Write down the first few terms of the infinite sequence:

                                            {n+3 /n² }^∞_n=1

               n=1 means that the sequence is starting from 1^st number and going till infinity                              ->  the expression value by substituting n=1,2,3,…!

                                            When n=1, (n+3)/n² =(1+3)/1^{2  ->} 4

                                            When n=2, (n+3)/n² =(2+3)/2^{2  ->} 5/4

                                           When n=3, (n+3)/n² =(3+3)/3^{2  ->} 6/9

                                           So the sequence goes like

                      

                                      {n+3 /n² }^∞_n=1 ={4,5/4,6/9,………..}

    General Series:

 

 

Example:   

 

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You can also Read our other blog Properties Exponential And Logarithmic Functions