Question

Will give medal
What is the sum of this infinite geometric series?

2 + 1 + 1/2+1/4+1/8…

Answer 1

Ignore the 2 for a sec,
that's kind of messing things up.

1 + 1/2+1/4+1/8…

So we have a common ratio of 1/2 yes?
We can write this as:\[\Large\rm \sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n\]

And if you recall, the convergent geometric series can be written as:\[\Large\rm \sum_{n=0}^{\infty}\left(r\right)^n=\frac{1}{1-r}\]

Answer 2

So then dealing with the 2,
I guess we have:
\[\Large\rm 2+\color{orangered}{\Large\rm \sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n}\]Which is:\[\Large\rm 2+\color{orangered}{\frac{1}{1-\frac{1}{2}}}\]Yes? :o

Answer 3

So, would the answer be 4? Or am I missing something?

Answer 4

Ooo I maybe messed up the numerator there >.< lemme check...

Answer 5

nonono I think that's right..
Yah 4 sounds right.

:)