9514 1404 393
Answer:
1/2
Explanation:
The base of the exponent tells us the common ratio of this geometric series is 1/2. The start value of n=7 tells us the first term in the series we're evaluating is ...
a1 = 2(1/2)^(7-4) = 2·(1/2)^3 = 2/8 = 1/4
The formula for the infinite sum of a geometric series is ...
S = a1(1/(1-r))
Filling in the values we know, this is ...
S = (1/4)(1/(1 -1/2)) = (1/4)(2) = 1/2
The infinite sum is 1/2.