\(3^2.2^4-2^3.4^2-2^3.5^0+4^2.2^2\)

\(=9.16-8.16-8.1+16.4\)

\(=16.\left(9-8\right)-8+64\)

\(=16.1-8+64\)

\(=8+64\)

\(=72\)

ĐA TẠ SƯ PHỤ VÕ NGỌC PHƯƠNG

a, A = 2 + 2.2 + 2.2.2 + 2.2.2.2 + ... + 2.2...2 ( 22...2 có 16 số 2)

A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶

2A = 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷

2A - A = ( 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷) - ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶)

A = 2¹⁷ - 2

b, B = 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28

1/2 x B = 1/2 + 1/6 + 1/12 + ... + 1/56

1/2 x B = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/7x8

1/2 x B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/7 - 1/8

1/2 x B = 1 - 1/8 = 7/8

B = 7/8 : 1/2

B = 7/8 x 2 = 7/4

a, A = 2 + 2.2 + 2.2.2 + 2.2.2.2 + ... + 2.2...2 ( 22...2 có 16 số 2)

A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶

2A = 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷

2A - A = ( 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷) - ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶)

A = 2¹⁷ - 2

b, B = 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28

1/2 x B = 1/2 + 1/6 + 1/12 + ... + 1/56

1/2 x B = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/7x8

1/2 x B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/7 - 1/8

1/2 x B = 1 - 1/8 = 7/8

B = 7/8 : 1/2

B = 7/8 x 2 = 7/4

2 . 2² . 2³ . 2⁴ . ... . 2²⁰¹⁶

= 2^{1+2+3+4+...+2016}

= 2^2033136

Đặt A = \(\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{2.2.2.....2}\)

          = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\)

=> 2A = \(2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\right)\)

           = \(2\times\frac{1}{2}+2\times\frac{1}{2^2}+2\times\frac{1}{2^3}+...+2\times\frac{1}{2^{50}}\)

           = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{49}}\)

 Lấy 2A - A = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{49}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\right)\)

               A  = \(1+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-...-\frac{1}{2^{50}}\)

                   = \(1-\frac{1}{2^{50}}\)

Vậy  \(\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{2.2.2.....2}\)=  \(1-\frac{1}{2^{50}}\)

1.  25 : 5,7 = 250/57

2.  30:2.8.4 = 480

3.  20:2^2.14= 70

4.  125:5^3.170= 170

5.  64:2^5.30.4=240

6.  (25:5^2.30): 15.7=14

       bạn à! Nhiều quá mình ko làm hết được. sorry nha.^-^                     

dù dài quá nhưng cố  gắng giúp mình làm hết nha