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Chapter 11: Problem 19

Evaluate the finite series for the specified number of terms. $$ 1+2+4+\ldots ; n=8 $$

Short Answer

Expert verified
The sum of the first 8 terms of the series is 255.

Step by step solution

01

Identify the values

Identify the first term (a), the common ratio (r), and the number of terms (n). In this series, the first term a is 1, the common ratio r is 2 (since each term is doubled), and the number of terms n is given as 8.
02

Plug the values into the formula

Substitute these values into the formula for the sum of a geometric series: \( S_n = a*(1 - r^n)/(1 - r) = 1*(1 - 2^8)/(1 - 2) \)
03

Calculate the sum

Calculate the sum by simplifying the expression. Since 2^8 is 256 and (1 - 256) gives -255, the equation becomes: \( S_n = 1*(-255)/-1 = 255 \)

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