cảm ơn nhaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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: 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:

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

\(A=1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+...+8}\)

= \(\frac{1}{\frac{1.2}{2}}+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{1}{\frac{8.9}{2}}\)

= \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)=2\left(1-\frac{1}{9}\right)=2.\frac{8}{9}=\frac{16}{9}\)

\(A=1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+...+8}\)

\(A=\frac{1}{\frac{1.2}{2}}+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{1}{\frac{8.9}{2}}\)

\(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\right)\)

\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)

\(A=2\left(1-\frac{1}{9}\right)=2.\frac{8}{9}=\frac{16}{9}\)

\(\text{Vậy A }=\frac{16}{9}\)

\(\text{#Hok tốt!}\)

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).

\(25\%-1\frac{1}{2}+0,5\cdot\frac{12}{5}\)   

\(=\frac{1}{4}-\frac{3}{2}+\frac{1}{2}\cdot\frac{12}{5}\)   

\(=\frac{1}{4}-\frac{3}{2}+\frac{6}{5}\)   

\(=\frac{5}{20}-\frac{30}{20}+\frac{24}{20}\)   

\(=\frac{-1}{20}\)

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