Answer:
The given geometric series is 2 + 4 + 8 + ...
We can see that the first term is 2 and the common ratio is 4/2 = 2.
The sum of a geometric series with a first term a and common ratio r, summed to n terms, is given by:
S_n = a(1 - r^n) / (1 - r)
Substituting the given values, we get:
a = 2
r = 2
n = 20
S_20 = 2(1 - 2^20) / (1 - 2)
S_20 = 2(1 - 1048576) / (-1)
S_20 = -2097150
Therefore, the sum of the given geometric series is -2097150.
Explanation:
The given geometric series is 2 + 4 + 8 + ...
We can see that the first term is 2 and the common ratio is 4/2 = 2.
The sum of a geometric series with a first term a and common ratio r, summed to n terms, is given by:
S_n = a(1 - r^n) / (1 - r)
Substituting the given values, we get:
a = 2
r = 2
n = 20
S_20 = 2(1 - 2^20) / (1 - 2)
S_20 = 2(1 - 1048576) / (-1)
S_20 = -2097150
Therefore, the sum of the given geometric series is -2097150.