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Igoryamba
3 years ago
11

What is the sum of the geometric series?

Mathematics
1 answer:
Dvinal [7]3 years ago
8 0

Essentially this is asking you to sum the first three values of the geometric series that starts with i being 1 and has the rule of (8(\frac{1}{4})^{i-1}).

Since we must sum the first <em>three </em>geometric values we need to see what the value of i will be for the first three. The sigma notation shows us that the first i will be equal to 1. This means the second i is 2 and the third i is 3.

Knowing this you can plug in the corresponding i values into (8(\frac{1}{4})^{i-1}) and sum it all together

(8(\frac{1}{4})^{1-1}) + (8(\frac{1}{4})^{2-1}) + (8(\frac{1}{4})^{3-1})

(8(\frac{1}{4})^{0}) + (8(\frac{1}{4})^{1}) + (8(\frac{1}{4})^{2})

(8(1)) + (8(\frac{1}{4})) + (8(\frac{1}{16}))

(8) + (2) + (\frac{1}{2}))

10 + \frac{1}{2})

\frac{21}{2})

10.5

Hope this helped!

~Just a girl in love with Shawn Mendes

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