Find the sum of the following series. Round to the nearest hundredth if necessary.

Mathematics

1 answer:

e-lub [12.9K]3 years ago

8 0

Answer:

11,184,808

Step-by-step explanation:

The n-th term of a geometric series is ...

an = a1·r^(n-1)

To fill in the formula, we need a1·r^n, so need to multiply the last term shown by r.

The value of r is 32/8 = 4, and the other terms of interest are a1 = 8, a1·r^(n-1) = 8388608. So, the sum is ...

$S_n=\dfrac{ra_1r^{n-1}-a_1}{r-1}=\dfrac{4\cdot 8,388,608-8}{4-1}=11,184,808$

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