Question

Tinh tổng:

S = 1/ 2 + 1 / 4 + 1 / 8 + ........+ 1/ 1024

Answer 1

      S= 1/2+1/2^2+1/2^3+.....+1/2^10

-    

      1/2x S =1/2^2+1/2^3+....+1/2^10+1/2^11

      1/2xS=1/2-1/2^11

       S=(1/2-1/2^11) :1/2

         =(1/2-1/2^11)x2

          = 1-1/2^10 =1-1/1024 =1023/1024

Answer 2

S=\(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

=> 2S=\(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

=> 2S - S = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

=> S = \(1-\frac{1}{2^{10}}\)

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