Cho a=2+2^2+2^3+…+2^30.Chung to rang a+2=2^31

0 bình luận về “Cho a=2+2^2+2^3+…+2^30.Chung to rang a+2=2^31”

1.   a=2+2^2+2^3+…+2^30

   ⇔ 2a=2^2+2^3+2^3+…+2^31

   ⇔ 2a-a=a=(2^2+2^3+2^3+…+2^31)-(2+2^2+2^3+…+2^30)

   ⇔ a=2^31-2

   ⇔ a+2=2^31

          Vậy a+2=2^31          (ĐPCM)

   Bình luận

2. Ta có :  

   $\begin{array}{l}
   a = 2 + {2^2} + {2^3} + {2^4} + {2^5} + … + {2^{30}}\\
    \Rightarrow 2.a = 2.\left( {2 + {2^2} + {2^3} + {2^4} + {2^5} + … + {2^{30}}} \right)\\
    \Rightarrow 2.a = {2^2} + {2^3} + {2^4} + {2^5} + {2^6} + … + {2^{31}}\\
    \Rightarrow 2.a – a = {2^2} + {2^3} + {2^4} + {2^5} + {2^6} + … + {2^{31}}\\
   \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, – \left( {2 + {2^2} + {2^3} + {2^4} + {2^5} + … + {2^{30}}} \right)\\
    \Rightarrow a = {2^2} + {2^3} + {2^4} + {2^5} + {2^6} + … + {2^{31}} – 2 – {2^2} – {2^3} – {2^4} – {2^5} – … – {2^{30}}\\
    \Rightarrow a = {2^{31}} – 2\\
    \Rightarrow a + 2 = {2^{31}} – 2 + 2\\
    \Rightarrow a + 2 = {2^{31}}
   \end{array}$

    

   Bình luận