How to find the limiting sum of the series: 81+27+9....
I kind of forgot..will appreciate if someone assisted me here since I have an exam in less than 2 days, thanks
A methodical way of approaching this question would be to ask oneself what is the sum of the geometric series. One will learn that the formula is
}{1-r})
which is simply
}{r-1})
but with both the numerator and the denominator multiplied by
Now, as one can see as
the sum becomes
noting that r is between -1 and 1.
Do you notice why the a stays in place? The reason is that a is the first term in the series and that r represents the rate of the series and n is the number of terms. A simple example would be to investigate this series
now does one notice that
is just
. To know where the a came from just multiply both sides by a and you are done.
Rest is plug and chug.
