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2 years ago

Application of Geometric Series

Mathematics

1 answer:

Gnoma [55]2 years ago

6 0

Answer:

7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

a1 = 2(0.6) . . . . . summation term for n=1

r = 0.6

So the sum is ...

$\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112$

Then the value of the entire given expression is ...

$\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}$

_____

A calculator can help you find the value.

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4 years ago

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Step-by-step explanation:

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