Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, write none. 4 + 3.2 + 2.56 + 2.048

Question

Find the sum of the infinite series if it exists.  If it exists, round to one decimal place.  If it does not exist, write none. 4 + 3.2 + 2.56 + 2.048

tkhunny · Answer

You must find the common ratio.  Let's see it.

anonymous · Answer

is it 0.8??

tkhunny · Answer

4*0.8 = 3.2
3.2*0.8 = 2.56
2.56*0.8 = 2.048

Looks like it.  Why do you doubt?

Now what?

anonymous · Answer

i doubt because im bad at math... but i dont know i wasnt there for this part so i didnt learn it

tkhunny · Answer

Well, stop it!  You're doing fine.  Whoever told you you were bad at math was just trying to discourage you.  Don't listen to it.  You should be learning.  A little bit of a struggle is not a bad thing at all.  I'm actually encouraged by it.  It means you are trying and you might even care!  :-)

Same things as all such infinite Geometric Series: $\dfrac{a_{0}}{1-r}$

$a_{0}$ is hte first term
$r$ is the common ratio.

If the ratio is between 1 and -1, it all converges and everything is fine!