Tính nhanh : (1/1.2 + 1/2.3 + …+1/1.10) .(1/1.2-1/2+1/1.3-1/3 +…+ 1/1.100 – 1/100)

Đáp án:

Giải thích các bước giải:

$\text{($\frac{1}{1.2}$ + $\frac{1}{2.3}$ +…+ $\frac{1}{1.10}$).($\frac{1}{1.2}$ – $\frac{1}{2}$ + $\frac{1}{1.3}$ – $\frac{1}{3}$ +…+$\frac{1}{1.100}$ – $\frac{1}{100}$)}$

$\text{ = ($\frac{1}{1.2}$ + $\frac{1}{2.3}$ +…+ $\frac{1}{1.10}$).($\frac{1}{2}$ – $\frac{1}{2}$ + $\frac{1}{3}$ – $\frac{1}{3}$ +…+$\frac{1}{100}$ – $\frac{1}{100}$)}$

$\text{= ($\frac{1}{1.2}$ + $\frac{1}{2.3}$ +…+ $\frac{1}{1.10}$).0 = 0}$