Question

Find the sum of the following infinite geometric series, if it exists. 1/2, 1/4, 1/8, 1/16,...

Answer 1

Well first the equation you will use is

Answer 2

\[S _{n}=\frac{ a(1-r^n) }{ 1-r }\]

Answer 3

\[a=\frac{ 1 }{ 2 }\]
\[r=\frac{ 1 }{ 2 }\]

Answer 4

Find
\[S_{n}\]

Answer 5

\[a _{1}/1-r ^{n}\] if \[\left| r \right|<1\] so there fore like aztec said r and a are 1/2 and 1/2

Answer 6

Then just substitute from there

Answer 7

Oh crap, it said infinite. @ronaldo7

Answer 8

\[S _{\infty}=\frac{ a(1-r^\infty) }{ 1-r }\]
When
\[\left| r \right|<1\]
And it is raised by the power of infinity, it will become so small and be close to zero.
That means r^infinity is zero.
\[S _{\infty}=\frac{ a(1-0) }{ 1-r }\]
\[S _{\infty}=\frac{ a }{ 1-r }\]