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Which of the following can be used to evaluate the series

Which of the following can be used to evaluate the series-example-1
Which of the following can be used to evaluate the series-example-1
Which of the following can be used to evaluate the series-example-2
Which of the following can be used to evaluate the series-example-3
User Nakosspy
by
8.3k points

1 Answer

2 votes

Answer:


5((1-((2)/(3) )^8)/(1-(2)/(3) ))

Explanation:

The given series is
\sum_(k=1)^85((2)/(3))^(k-1)

We want to write an expression that can be used to evaluate this series.

Since this is a geometric series, we use the formula for the sum of the first k terms.


S_k=a((1-r^k)/(1-r))

From the given series the first term is
a=5 and the common ratio is
r=(2)/(5) and k=8

We substitute the values to obtain:


S_8=5((1-((2)/(3) )^8)/(1-(2)/(3) ))

User Fernando Ferreira
by
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