If $2^{20}=1048576$ , what is $2^1+2^2+2^3+...+2^{18}+2^{19}?$

1048573
1048576
1048574
1048575

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Applying the geometric series formula:

$1(\frac{1-2^{20}}{1-2}) - 2^0 = 1048574$

Also $2^0+2^1+2^2+2^3+...+2^n=2^{n+1}$ . For this problem, you are supposed to use the fact (derived from the previous fact) that $2^1+2^2+2^3+..+2^n=2^{n+1}-2^0=2^{n+1}-1$ .