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

Evaluate the geometric series. Round to the nearest hundredth. Help me please!!-example-1
User Volpav
by
8.0k points

1 Answer

6 votes

Answer:

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 )

User Akuma
by
8.1k points

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