Explicație pas cu pas:
[tex]\bf B=2^0 + 2^1 +2^2 +2^{3}+2^{4}+2^{5} + ....+2^{2003}[/tex]
[tex]\bf B=\Big(2^0 + 2^1 +2^2 +2^{3}\Big)+\Big(2^{4}+...+2^{7}\Big)+ ...+\Big(2^{2000}+... +2^{2003}\Big)[/tex]
[tex]B=\Big(1+ 2 +4 +8\Big)+2^{4}\cdot\Big(2^{4-4}+...+2^{7-4}\Big)+ ...+2^{2000}\cdot\Big(2^{2000-2000}+... +2^{2003-2000}\Big)[/tex]
[tex]\bf B=15+2^{4}\cdot\Big(2^{0}+2^1 +2^2 +2^{3}\Big)+ ...+2^{2000}\cdot\Big(2^{0}+2^1 +2^2 +2^{3}\Big)[/tex]
[tex]\bf B=15+2^{4}\cdot\Big(1+ 2 +4 +8\Big)+ ...+2^{2000}\cdot\Big(1+ 2 +4 +8\Big)[/tex]
[tex]\bf B=15+2^{4}\cdot 15+ ...+2^{2000}\cdot 15[/tex]
[tex]\red{\boxed{~\bf B=15\cdot\Big(2^{0}+2^{4}+2^{8}+... +2^{2000}\Big)~~\vdots~~15~}}[/tex]
[tex]==pav38==[/tex]
