Question

determaine the sum, if there is one, of the infiite geometric series: 4+4/3+4/9+4/27+...

Answer 1

Well we have the first term...4....and do you know what r (the common ratio) would be here?

Answer 2

In case you are not there...I'll just walk you through it....we can see that each time...the previous number is being divided by 3....since geometric sequences only deal with multiplication....this is the same as 1/3

so our:
a = 4
r = 1/3

We can use the equation for an infinite sum

\[\sum_{k=0}^{\infty} (a \frac{ 1 }{ 1-r })\]

so after plugging in the numbers we have

\[\sum_{k=0}^{\infty} (4 \frac{ 1 }{ 1-\frac{ 1 }{ 3 } })\]

So doing that out we can see

1 1
----- = --------- 1.5
1 - (1/3) 2/3

So 4 * 1.5 = 6

So the infinite sum here....would = 6

Hope that helps!