sum of infinite geometric series 9/4+3/2+1+2/3+... solution
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Step-by-step explanation:
1 Answer
George C.
Oct 22, 2016
1
+
2
3
+
4
9
+
...
=
3
Explanation:
The general term of any geometric series can be written in the form:
a
n
=
a
⋅
r
n
−
1
for
n
=
1
,
2
,
3
,
...
where
a
is the initial term and
r
the common ratio
In our case we have:
a
n
=
1
⋅
(
2
3
)
n
−
1
for
n
=
1
,
2
,
3
,
...
with initial term
a
=
1
and common ratio
r
=
2
3
The general formula for the infinite sum (proved below) is:
∞
∑
n
=
1
a
r
n
−
1
=
a
1
−
r
when
|
r
|
<
1
So in our case:
∞
∑
n
=
1
1
⋅
(
2
3
)
n
−
1
=
1
1
−
2
3
=
1
1
3
=
3
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