What is the sum of the geometric series 10 sigma n=1 6(2)^n

12276

Solution:

Explanation:
This expression can be written as:
Σ
10
i
=
1
(
6
×
2
n
)
=
6
×
Σ
10
i
=
1
2
n

The last expression is a sum of a finite geometrical sequence for which:
a
1
=
2
,
q
=
2
,
n
=
10
. This sum can be calculated as:
S
10
=
2
×
1
−
2
10
1
−
2
=
2
×
2
10
−
1
2
−
1
=
2
×
(
2
10
−
1
)
=
=
2
×
1023
=
2046
So the value of the first expression is:
6
×
2046
=
12276