\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)....\left(1-\frac{1}{2007^2}\right)=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{4028049}\right)=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{4028048}{4028049}=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{2006.2008}{2007.2007}=\frac{1.2.3...2006}{2.3.4...2007}.\frac{3.4.5....2008}{2.3.4....2007}=\frac{1}{2007}.\frac{2008}{2}=\frac{1}{2007}.1004=\frac{1004}{2007}\)Tích và theo dõi mk nhé

Chúc bạn học tốt

\(Giải:\)

\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+.......+\frac{1}{20}\left(1+.......+20\right)\)

\(B=1+\frac{1}{2}\left(\frac{3.2}{2}\right)+\frac{1}{3}\left(\frac{4.3}{2}\right)+\frac{1}{4}\left(\frac{5.4}{2}\right)+.......+\frac{1}{20}\left(\frac{21.20}{2}\right)\)

\(B=1+\frac{3.2}{2.2}+\frac{4.3}{3.2}+\frac{5.4}{4.2}+.........+\frac{21.20}{20.2}\)

\(B=1+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+.........+\frac{21}{2}=\frac{1}{2}+\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+.........+\frac{21}{2}-\frac{1}{2}\)

\(=\frac{1+2+3+.........+21-1}{2}=\frac{22.21-1}{4}=\frac{242-1}{4}=\frac{241}{4}=60\frac{1}{4}\)

Bài 1:

1) \(\frac{11}{3}\): 3\(\frac{1}{3}\)- 3

= \(\frac{11}{3}\): \(\frac{10}{3}\)- 3

= \(\frac{11}{3}\). \(\frac{3}{10}\)- 3 

= \(\frac{11}{10}\)- 3

= \(\frac{-19}{10}\)

2) \(\frac{5}{6}\):  \(\frac{3}{52}\) - \(\frac{5}{6}\). 47\(\frac{1}{3}\)

= \(\frac{5}{6}\) . \(\frac{52}{3}\)- \(\frac{5}{6}\). 47\(\frac{1}{3}\)

= \(\frac{5}{6}\).(\(\frac{52}{3}\)- 47\(\frac{1}{3}\))

= \(\frac{5}{6}\).( -30)

= -25

mách mình mấy câu kia với

kinh!

oOo Hello the world oOo, làm được không?

Cố gắng lên, mấy thánh sẽ phù hộ con!!!

thánh rảnh thì thánh giải hộ con với 

\(\frac{1}{x}+\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+...+\frac{1}{\left(x+9\right)\left(x+10\right)}\)

\(=\frac{1}{x}+\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+...+\frac{1}{x+9}-\frac{1}{x+10}\)

\(=\frac{2}{x}-\frac{1}{x+10}=\frac{2\left(x+10\right)}{x\left(x+10\right)}-\frac{x}{x\left(x+10\right)}=\frac{2x+20-x}{x\left(x+10\right)}=\frac{x+20}{x^2+10x}\)

lớp 8 hẽ

TL:

a)

\(\frac{14\left(x-3\right)}{21}+\frac{7\left(x-5\right)}{21}=\frac{13x+4}{21}\) 

\(\frac{14x-42+7x-35}{21}=\frac{13x+4}{21}\) 

21x-77=13x+4

21x-13x=77+4

8x=81

x=\(\frac{81}{8}\) 

2 câu còn lại bn lm cách tương tự 

hc tốt