To find the sum of the series A=4+2²+2³+2⁴+...+2²⁰, we can use the formula for the sum of a geometric series.

The formula for the sum of a geometric series is given by:

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

Where:
S = sum of the series
a = first term of the series
r = common ratio
n = number of terms

In this case, the first term (a) is 4, the common ratio (r) is 2, and the number of terms (n) is 20.

Plugging these values into the formula, we get:

S = 4 * (2^20 - 1) / (2 - 1)

Simplifying further:

S = 4 * (1048576 - 1) / 1

S = 4 * 1048575

S = 4194300

Therefore, the sum of the series A=4+2²+2³+2⁴+...+2²⁰ is 4194300.