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
Evaluate ∑
(1
2)𝑟
∞
𝑟=1
A. 2
B. 1
C. 0.5.
D. 0.25
1 answer