co \(\frac{1}{9\cdot10}=\frac{1}{9}-\frac{1}{10}\)

\(\frac{1}{10\cdot11}=\frac{1}{10}-\frac{1}{11}\)

............

\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}-\frac{1}{x+1}\)

nen \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\)

\(=\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}-...+\frac{1}{x}-\frac{1}{x+1}\)

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

2 .  ( \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\))

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

Bạn ơi tim x mà bạn

bo may ko biet

\(M=\dfrac{15}{7\cdot8}-\dfrac{17}{8\cdot9}+\dfrac{1}{9\cdot10}+\dfrac{1}{10\cdot11}\)

\(M=\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\)

\(M=\dfrac{1}{7}-\dfrac{1}{11}=\dfrac{11-7}{7\cdot11}=\dfrac{4}{77}\)

`M=15/(7.8)-17/(8.9)+1/(9.10)+1/(10.11)`

`=1/7-1/8-(1/8-1/9)+1/9-1/10+1/10-1/11`

`=1/7-1/4+2/9-1/11`

`=67/2772`

Theo mình đề bài sai phải là `M=15/(7.8)-17/(8.9)+1/(9.10)+1/(10.11)`

`=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11`

`=1/7-1/11=4/77`

M=18+17−18−19+19−110+110−111M=18+17−18−19+19−110+110−111

\(\frac{7}{3.4}-\frac{9}{4.5}+\frac{11}{5.6}-\frac{13}{6.7}+\frac{15}{7.8}-\frac{17}{8.9}-\frac{19}{9.10}+\frac{21}{10.11}\)

\(=\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}-\frac{9+10}{9.10}+\frac{10+11}{10.11}\)

\(=\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}-\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}-\frac{1}{8}-\frac{1}{9}+\frac{1}{9}+\frac{1}{10}-\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{3}-\frac{1}{11}=\frac{8}{33}\)

1003002000

cách giải ?

Câu hỏi của Phung Ngoc Quoc Bao - Toán lớp 6 - Học toán với OnlineMath

Cách thực hiện y hệt 

giai dum voi dang nay minh lam lan dau tien len khong biet

Nhan B voi 3 ta duoc:

3B=9.10.3+10.11.3+11.12.3+.....+98.99.3

3B=9.10.(11-8)+10.11.(12-9)+11.12.(13-3)+.....+98.99.(100-97)

3B=(9.10.11-8.9.10)+(10.11.12-9.10.11)+(11.12.13-10.11.12)+.....+(98.99.100-97.98.99)

3B=98.99.100-8.9.10=970200-720=969480

B=969480:3=323160

ok roi ban nhe!

 \(\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{89.90}\)

= \(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+....+\frac{1}{89}-\frac{1}{90}\)

= \(\frac{1}{9}-\frac{1}{90}\)

=\(\frac{1}{10}\)