1.Rút gọn ps $\frac{75}{1000}$ 2.Tính nhanh: a.1/8+1/16+1/32+…+1/1024 b.1-1/16-1/32-…-1/1024 c.4/5×7+4/7×9+…+4/53×55 d.476×934-218/933×476+23

Bài 1:

$\frac{75}{1000}$ = $\frac{3 × 25}{40 × 25}$ = $\frac{3}{40}$

Bài 2:

a, Đặt $\frac{1}{8}$ + $\frac{1}{16}$ + … + $\frac{1}{1024}$ = A ta có:

      A = $\frac{1}{8}$ + $\frac{1}{16}$ + … + $\frac{1}{1024}$

⇔ A = $\frac{1}{2^3}$ + $\frac{1}{2^4}$ + … + $\frac{1}{2^{10}}$

⇔ $\frac{1}{2}$A = $\frac{1}{2^4}$ + $\frac{1}{2^5}$ + … + $\frac{1}{2^{11}}$

⇔ A – $\frac{1}{2}$A = ($\frac{1}{2^3}$ + … + $\frac{1}{2^{10}}$) – ($\frac{1}{2^4}$ + … + $\frac{1}{2^{11}}$

⇔ $\frac{1}{2}$A = $\frac{1}{2^3}$ – $\frac{1}{2^{11}}$

⇔ $\frac{1}{2}$A = $\frac{1}{8}$ – $\frac{1}{2048}$

⇔ $\frac{1}{2}$A = $\frac{255}{2048}$

⇔ A = $\frac{255}{1024}$

c, $\frac{4}{5 × 7}$ + $\frac{4}{7 × 9}$ + … + $\frac{4}{53 × 55}$

= 2($\frac{2}{5 × 7}$ + $\frac{2}{7 × 9}$ + … + $\frac{2}{53 × 55}$)

= 2($\frac{7-5}{5 × 7}$ + $\frac{9-7}{7 × 9}$ + … + $\frac{55-53}{53 × 55}$)

= 2($\frac{7}{5 × 7}$ – $\frac{5}{5 × 7}$ + $\frac{9}{7 × 9}$ – $\frac{7}{7 × 9}$ + … + $\frac{55}{53 × 55}$ + $\frac{53}{53 × 55}$)

= 2($\frac{1}{5}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{9}$ + … + $\frac{1}{53}$ – $\frac{1}{55}$)

= 2($\frac{1}{5}$ – $\frac{1}{55}$)

= 2($\frac{11}{55}$ – $\frac{1}{55}$)

= 2 × $\frac{2}{11}$

= $\frac{4}{11}$