Question

Evaluate the geometric series. Round to the nearest hundredth. Help me please!!

Answer 1

7.50

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

5
`((1)/(3)) ^(n-1)` is the n th term of a geometric series

with a = 5 and r =
`(1)/(3)`

The sum to n terms of a geometric series is

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

`S_(10)` =
`(5(1-(((1)/(3)) ^(10)) )/(1-(1)/(3) )`

=
`(5(1-(1)/(59049)) )/((2)/(3) )`

=
`(5((59048)/(59049)) )/((2)/(3) )`

=
`(15)/(2)` × 0.9999..

= 7.5 × 0.9999...

≈ 7.50 ( to the nearest hundredth )