What is the sum of the first 10 terms of the Geometric Serie: 4 + 16 + 64 + ... + 4^10

This is a geometric sequence with initial term

1

and common ratio

4

:

a

1

=

1

a

n

=

a

1

⋅

4

n

-

1

=

4

n

-

1

10

∑

n

=

1

4

n

-

1

=

1

3

(

4

-

1

)

10

∑

n

=

1

4

n

-

1

=

1

3

(

4

10

∑

n

=

1

4

n

-

1

-

10

∑

n

=

1

4

n

-

1

)

=

1

3

(

11

∑

n

=

2

4

n

-

1

-

10

∑

n

=

1

4

n

-

1

)

=

1

3

⎛

⎝

4

10

+

10

∑

n

=

2

4

n

-

1

-

1

-

10

∑

n

=

2

4

n

-

1

⎞

⎠

=

1

3

(

4

10

-

1

)

=

1

3

(

2

20

-

1

)

=

1

3

(

1048576

-

1

)

#=1048575/3#

=

349525