Question

What is the sum of the geometric series?

Answer 1

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 three 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