Question

Evaluate the geometric series. Please help me!!

Answer 1

- 85

Explanation:

The n th term of a geometric series is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

1
`(-2)^(n-1)` ← is the n th term of a geometric series

with a = 1 and r = - 2

The sum to n terms of a geometric series is

`S_(n)` =
`(a(r^(n)-1) )/(r-1)`

=
`(1((-2)^(8)-1 )/(-2-1)`

=
`(256-1)/(-3)`

=
`(255)/(-3)`

= - 85