Question

2^0+2^1+2^2+...+2^2001=?

Answer 1

[tex]S=2^0+2^1+2^2+...+2^{2001}\\ [/tex]

Inmultim relatia cu 2:

$2S = 2^1+2^2+2^3...+2^{2001}+2^{2002}$

Dupa cum observi, toti termenii, mai putin ultimul, fac parte din S:

[tex]2S =(S-2^0)+2^{2002}\\ 2S=S+2^{2002}-1\\ S=2^{2002}-1[/tex]