Question

Find the sum of the geometric series. 0.25, 0.5, 1, 2, ..., 256.

a) 511
b) 256
c) 255
d) 257

Answer 1

To find the sum of the given geometric series, use the formula for the sum of a geometric series.

Step-by-step explanation:

To find the sum of the given geometric series, we can use the formula for the sum of a geometric series:

S = a(1 - r^n)/(1 - r)

Where:

• S is the sum of the series
• a is the first term
• r is the common ratio
• n is the number of terms

In this case, the first term (a) is 0.25, the common ratio (r) is 2, and the number of terms (n) can be found by solving the equation 0.25 * 2^(n-1) = 256. Solving this equation gives us n = 9. Now we can plug these values into the formula:

S = 0.25 * (1 - 2^9)/(1 - 2)

Simplifying this gives:

S = 0.25 * (511)/(1 - 2)

S = 0.25 * (-511)

S = -127.75

Therefore, the sum of the geometric series is -127.75.