Question

Find the indicated sum for the geometric series.
S6 for 2 +1 + 1/2 + 1/4 + ...

Answer 1

okay, so here we just need to find 2 more terms, right? then add them all up!

Answer 2

Okay. How would we find the next 2? @robz8

Answer 3

well, since it is a geometric series, what is the pattern we see between each of the numbers?

Answer 4

Its being subtracted? @robz8

Answer 5

hmm noooo... not quite... remember, a geometric series means that we are multiplying each number by something to get the next number!

what number number to we multiply to 2 to get 1?

how about from 1 to 1/2?

Answer 6

.5 @robz8

Answer 7

exactly! so just keep multiplying the numbers by .5 (or 1/2) to get the next to numbers in the series!

Answer 8

I got 1/8 and 1/16. @robz8

Answer 9

And for my final answer, I got 63/16

Answer 10

you are supposed to be adding up forever

Answer 11

doesn't S6 determine that it is the summation up the the 6th term right?

Answer 12

her syntax was a little confusing

Answer 13

\[a+ar+ar^2+ar^3+ar^4+...=\frac{a}{1-r}\] ah i see, it does say \(S_6\) but then it has the \(...\) hmmm

Answer 14

if it is six terms, add

Answer 15

yeah if it was an infinite geometric series then it would be 2/(1-(1/2)), but i don't think that' what it's asking

Answer 16

you are correct, it is 63/16. good job! @Emilyh117

Answer 17

Thanks! :) @robz8