Math 11 Week #2

This week, I learned how to tell if a geometric sequence or series is converging or diverging. Converging is when you can find an infinite sum, whereas diverging is when there is no infinite sum.

The rule to know if the sequence is diverging is if:
$1<r$

$-1>r$

The rule to know if the sequence is converging

$-1<r<1$

ex. If we are given a geometric sequence such as: $1, \frac{1}{3},\frac{1}{9},\frac{1}{27}$ and $r= \frac{1}{3}$

We know that this sequence is converging and will have an infinite sum because $-1<r<1$

To find the infinite sum we use the equation:

S∞= $\frac{a}{1-r}$

Now insert the numbers :

S∞= $\frac{1}{1-\frac{1}{3}}$

S∞= $\frac{3}{2}$

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