We have:
Quantity A: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}+ a_{20}\)
Quantity B: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}\)

Subtract \((a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19})\) from both quantities to get:
Quantity A: \(a_{20}\)
Quantity B: \(0\)


GIVEN: \(a_n=2^n -\frac{1}{2^{n-21}}\)

So, \(a_{20}=2^{20} -\frac{1}{2^{20-21}}=2^{20} -\frac{1}{2^{-1}}=2^{20} - 2^{1} =\) (a very very big number) - 2

We get:
Quantity A: (a very very big number) - 2
Quantity B: 0

Answer: A

Cheers,
Brent