2 to the power

Algebra Level pending

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

1048573 1048576 1048574 1048575

1 solution

J L
Jul 21, 2020

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 $2^1+2^2+2^3+..+2^n=2^{n+1}-2^0=2^{n+1}-1$ .

I included $2^0$ as well :(

Mahdi Raza - 10 months, 2 weeks ago

Oh. I understand, I previously posted this and there was an error so I re-posted it here. The $2^0$ was an unintentional trick until I re-posted the problem.

J L - 10 months ago

Oh no no, I hadn't solved the error one. I just did a mistake here

Mahdi Raza - 10 months ago

@Mahdi Raza – Ok. That's what I thought, but ok.

J L - 10 months ago

2 to the power

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