Question

[Hoàng Thị Thanh Huyền]

Thực hiện phép tính sao cho nhanh nhất 

a,\(1\frac{1}{5}.0,75-\frac{6}{7}.1\frac{1}{3}+\frac{6}{7}\)                                    b, \(2017.2018.\left(\frac{2016}{2017}-\frac{2016}{2018}\right)\)

c,\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right).......\left(\frac{1}{100}-1\right)\)                        d,\(\frac{1023}{2^1+2^2+......2^{10}}\)    

Answer 1

[Justice Soul]

d,  \(\frac{1023}{2^1+2^2+...+2^{10}}\)

\(\text{Đặt}:S=2^1+2^2+...+2^{10}\)

\(2S=2.\left(2^1+2^2+..+2^{10}\right)\)

\(2S=2^2+2^3+..+2^{11}\)

\(S=2S-S=\left(2^2+2^3+...+2^{11}\right)-\left(2^1+2^2+...+2^{10}\right)\)

\(S=2^{11}-2^1=2^{11}-1\)

Thay S vào biểu thức \(\frac{1023}{2^1+2^2+...+2^{10}}\),ta được 

\(\frac{1023}{2^{11}-1}=\frac{1023}{2047}\)

Vậy ......