Evaluate ∑

(1
2)𝑟

𝑟=1
A. 2
B. 1
C. 0.5.
D. 0.25

1 answer

We can begin by writing out the terms of the series:

(1/2)^1 + (1/2)^2 + (1/2)^3 + ...

Notice that this is a geometric series with first term 1/2 and common ratio 1/2. Thus, we can use the formula for the sum of an infinite geometric series:

∑(1/2)^r = a/(1 - r)

where a is the first term and r is the common ratio. Plugging in a = 1/2 and r = 1/2, we get:

∑(1/2)^r = (1/2)/(1 - 1/2) = 1

Therefore, the sum of the series is 1.

Answer: B. 1