Question

Tính giá trị của biểu thức 

\(M=512-\frac{512}{2}-\frac{512}{2^2}-\frac{512}{2^3}-...-\frac{512}{2^{10}}\)

Làm rõ từng bước giúp mình vs

 

Answer 1

M = 512 - 512/2 - .... - 512/2^10

   = 2^9 - 2^9 / 2 - 2^9/2^2 - ...2^9/2^10

   = 2^9 - 2^8 - 2^7 - 2^6 -.... - 1/2

2M = 2^10 - 2^9 - 2^8 - .... - 1 

2M - M = 2^10 - 2^9 - 2^8 -... -1 - 2^9  + 2^8 + 2^7 +... +    1 + 1/2

          M   = 2^10 - 2.2^9 + 1/2

          M  = 2^10 - 2^10 + 1/2

          M  = 1/2

Answer 2

M = 512 - 512/2 - .... - 512/2^10
   = 2^9 - 2^9 / 2 - 2^9/2^2 - ...2^9/2^10
   = 2^9 - 2^8 - 2^7 - 2^6 -.... - 1/2
2M = 2^10 - 2^9 - 2^8 - .... - 1 
2M - M = 2^10 - 2^9 - 2^8 -... -1 - 2^9  + 2^8 + 2^7 +... +    1 + 1/2
          M   = 2^10 - 2.2^9 + 1/2
          M  = 2^10 - 2^10 + 1/2
          M  = 1/2

Answer 3

NÈ :

Bùi Nguyễn Việt Anh

Answer 4

 yamamoto

Answer 5

\(\text{M = 512 - 512/2 - .... - 512/2^10}\)

   \(\text{= 2^9 - 2^9 / 2 - 2^9/2^2 - ...2^9/2^10}\)

   \(\text{= 2^9 - 2^8 - 2^7 - 2^6 -.... - 1/2}\)

\(\text{2M = 2^10 - 2^9 - 2^8 - .... - 1}\)

 \(\text{ 2M - M = 2^10 - 2^9 - 2^8 -... -1 - 2^9 + 2^8 + 2^7 +... + 1 + 1/2}\)

          \(\text{M = 2^10 - 2.2^9 + 1/2}\)

        \(\text{ M = 2^10 - 2^10 + 1/2}\)

          \(M=\frac{1}{2}\)

Answer 6

 Haibara Ai

Answer 7

M=1/2