Find the sum of the following infinite
geometric series. Use a formula and
show your work.
(100)+(-40)+(16)+(-32)+etc...forever
5
Hint: r = (-2)
5
thats -32/5.... and on the hint is -2/5
Do you mean its -$\displaystyle 32/5$?
Since the hint says to try $\displaystyle r =-2/5$, we can plug that in to our values and see what happens
$\displaystyle 100(-2/5) = -40$
$\displaystyle
-40(-2/5) = 16
$
So we see that each term is changing by a factor of $\displaystyle -2/5$. Now we know the equation for a geometric series is $\displaystyle a/(1-r), $where a is the first term and r is the ratio. Plug in the first term in the series for a, and plug in the ratio r, and then solve the equation to find the sum of the series.
Hello, Steph07!
Find the sum of the following infinite geometric series:
. . $\displaystyle 100 -40 + 16 - \tfrac{32}{5} + \hdots$
You're expected to know the formula . . .
. . $\displaystyle S \;=\;\frac{a}{1-r}$ . . . where $\displaystyle a$ is the first term and $\displaystyle r$ is the common ratio.
We have: .$\displaystyle a = 100,\;r = \text{-}\tfrac{2}{5}$
Plug them into the formula . . .