A=3/2-5/6+/12-9/20+11/30-13/42+15/56-17/72+19/90

A=11/10

hok tốt nha

Cái này tôi thấy ko có tính nhanh đc 

bấm máy đi :))

Ra \(\frac{76}{405}\)

a: \(\dfrac{33}{x}=\dfrac{y}{8}=\dfrac{z}{160}=\dfrac{45}{120}\)

=>33/x=y/8=z/160=3/8

=>x=88; y=33; z=60

b: \(\dfrac{x}{3}=\dfrac{14}{y}=\dfrac{z}{60}=\dfrac{-8}{12}=-\dfrac{2}{3}\)

nên x=-2; y=-21; z=-40

a)Quy đồng: \(\frac{5}{8}=\frac{5.3}{8.3}=\frac{15}{24}\)

Vì \(\frac{5}{24}< \frac{10+5}{24}=\frac{15}{24}\)

\(\Rightarrow\frac{5}{24}< \frac{5+10}{24}=\frac{5}{8}\)

b) Quy đồng:

\(\frac{4}{9}=\frac{4.6}{9.6}=\frac{24}{9.6}\)

\(\frac{2}{3}=\frac{2.18}{3.18}=\frac{36}{9.6}\)

Vì \(\frac{36}{9.6}>\frac{24}{9.6}>\frac{6+9}{9.6}\)

\(\Rightarrow\frac{2}{3}>\frac{4}{9}>\frac{6+9}{6.9}\)

Có \(P=\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times...\times\frac{399}{400}< \frac{2}{3}\times\frac{4}{5}\times...\times\frac{400}{401}\)

=> \(P^2< \frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{400}{401}=\frac{1}{401}< \frac{1}{400}=\frac{1}{20}\)

=> \(P< \frac{1}{20}\)(đpcm).

a: Ta có: \(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(=-\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\cdots+\frac{1}{9\cdot10}\right)\)

\(=-\left(\frac14-\frac15+\frac15-\frac16+\cdots+\frac19-\frac{1}{10}\right)=-\left(\frac14-\frac{1}{10}\right)=-\frac{3}{20}\)

a)121212/424242=2/7

1999999999/9999999995=1/5

Sorry bạn mik chỉ bt làm câu a thôi!

HT~

Câu b:

\(\frac{a}{b}:\frac{c}{d}=\frac{ad}{bc}=\frac{6}{5}\Leftrightarrow5ad=6bc\)

\(\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}=\frac{1}{15}\Leftrightarrow5\left(ad-bc\right)=\frac{bd}{3}\)

\(\Rightarrow5ad-5bc=\frac{bd}{3}\)

Thay vào ta có:

\(\frac{a}{b}-\frac{c}{d}=\frac{a}{b}-\frac{1}{3}=\frac{1}{15}\Leftrightarrow\frac{a}{b}=-\frac{4}{15}\)