Write out the first four terms of the series to show how the series starts. Then find the sum of the series or show that it diverges. Summation from n equals 0 to infinity (StartFraction 9 Over 7 Superscript n EndFraction plus StartFraction 3 Over 5 Superscript n EndFraction )

The first four terms of the series are

= 14.25

Step-by-step explanation:

We know that

Sum of convergent series is also a convergent series.

We know that,

If the common ratio of a sequence |r| <1 then it is a convergent series.

The sum of the series is

Given series,

The first four terms of the series are

Let

   and    

Now for ,

It is a geometric series.

The common ratio of is

The sum of the series

    =10.5

Now for

It is a geometric series.

The common ratio of is

The sum of the series

    =3.75

The sum of the series is

                                        =

                                       =10.5+3.75

                                       =14.25

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