Question

Tính nhanh:     A= \(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+....+\(\frac{1}{2^{10}}\)

Answer 1

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

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

2A - A = \(1-\frac{1}{2^{10}}\)

=> A = \(1-\frac{1}{2^{10}}\)

Answer 2

 Ta có : A = 1/2 +1/2^2 + 1/2^3 + ... + 1/2^10

           2A = 2 ( 1/2 +1/2^2 + 1/2^3 + ... + 1/2^10 )

           2A = 1 + 1/2 + 1/2^2 + ... + 1/2^9

           2A - A = A = ( 1 + 1/2 + 1/2^2 + ... + 1/2^9 ) - ( 1/2 + 1/2^2 + 1/2^3 +... + /2^10 )

                           =  1 - 1/2^10 = ...

Answer 3

Ta có:  a=1/2+1/2²+......+1/2¹⁰

              2a=1+1/2+1/2²+.......+1/2⁹

          =>2a-a=1-2¹⁰

           =1023/1024