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+238
Giúp mk gấp.Help me
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+238
Giúp mk gấp.Help me
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 × $\frac{2}{11}$
= $\frac{4}{11}$