We can rewrite the given expression as:

A = 2^0 + 2^1 + 2^2 + 2^3 + ... + 2^19 + 2^20

This is a geometric series with a common ratio of 2. The sum of a geometric series can be found using the formula:

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

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2^0 = 1, r = 2, and n = 21 (since we have 21 terms from 2^0 to 2^20).

Plugging these values into the formula, we get:

A = 1 * (2^21 - 1) / (2 - 1)
A = (2^21 - 1)

Using the exponent rule that 2^x - 1 = 2^(x-1) + 2^(x-2) + ... + 2^2 + 2^1 + 2^0, we can simplify further:

A = (2^20 + 2^19 + 2^18 + ... + 2^2 + 2^1 + 2^0) + 1
A = (2^20 + 2^19 + 2^18 + ... + 2^2 + 2^1 + 2^0) + 1
A = (2^20 + 2^19 + 2^18 + ... + 2^2 + 2^1 + 2^0) + 1

Therefore, A = (2^20 + 2^19 + 2^18 + ... + 2^2 + 2^1 + 2^0) + 1.