Question

Application of Geometric Series

Answer 1

7.2224

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)(1-0.6^4)/(1-0.6)=(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}`

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A calculator can help you find the value.