Explicație pas cu pas:
[tex]a = {2}^{1} + {2}^{3} + {2}^{5} + ... + {2}^{81} = \\ [/tex]
[tex]= 2(1 + {2}^{2} + {2}^{4} + {2}^{6} + ... + {2}^{80}) \\ [/tex]
[tex]= 2(1 + {({2}^{2})}^{1} + { ({2}^{2}) }^{2} + {({2}^{2})}^{3} + ... + {({2}^{2})}^{40}) \\ [/tex]
[tex]= 2({(4)}^{0} + {(4)}^{1} + { (4) }^{2} + {(4)}^{3} + ... + {(4)}^{40}) \\ [/tex]
[tex]= 2b[/tex]
=>
[tex]\frac{a}{b} = \frac{2b}{b} = 2 \\ [/tex]
