Question

Find the the sum for the shown infinite geometric series? 2,2/3, 2/9, ...

Answer 1

Answer:

3

Step-by-step explanation:

The formula for the sum of an infinite geometric series is

$\frac{a}{1-r}$

Where a is the first term and r is the common ratio. We can see that the first term is 2, and to find the common ratio, we can divide a term by the one before it. We can get:

$\frac{\frac{2}{3}}{2} =\frac{2}{3} *\frac{1}{2}=\frac{1}{3}$

Now, we have all the values need to evaluate the formula. We can plug them in:

$\frac{2}{1-\frac{1}{3} } \\\frac{2}{\frac{2}{3} } \\2*\frac{3}{2}\\3$