[tex] 2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=
=[tex]1+ 1 + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} [/tex]=
=[tex]2* 2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} [/tex]=
=[tex] 2^{1} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=
=[tex]2* 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=
=[tex] 2^{2} + 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=
=[tex]2* 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=
..................................
=2*[tex] 2^{10} [/tex]=[tex] 2^{11} [/tex]
sau, asa cum a scris respondentul anterior, folosesti formula:
[tex] 2^{n+1} - 1= (2-1)( 2^{n} + 2^{n-1} + 2^{n-2} +.....+ 2^{1} + 2^{0} )[/tex], adica:
[tex] 2^{11} - 1= (2-1)( 2^{10} + 2^{9} + 2^{8} +.....+ 2^{1} + 2^{0} )[/tex] deci:
[tex] 2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1[/tex]=[tex] 2^{11} [/tex]
