a, A = 1.2 + 2.3 + 3.4 + 4.5 + 5.6 + 6.7 + 7.8 + 8.9 + 9.10 + 10.11

= (1.2 + 2.3) + (3.4 + 4.5) + (5.6 + 6.7) + (7.8 + 8.9) + (9.10 + 10.11)

= 2( 1 + 3) + 4( 3 + 5) + 6( 5 + 7) + 8 ( 7 + 9) + 10( 9 + 11)

= 2.4 + 4.8 + 6.12 + 8.16 + 10.20 = 2.2.2 + 2.4.4 + 2.6.6 + 2.8.8 + 2.10.1

b,tương tự nhé

\(\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}\)

\(=\frac{8-7}{7\cdot8}+\frac{9-8}{8\cdot9}+\frac{10-9}{9\cdot10}+\frac{11-10}{10\cdot11}+\frac{12-11}{11\cdot12}+\frac{13-12}{12\cdot13}\)

\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}\)

\(=\frac{1}{7}-\frac{1}{13}=\frac{13-7}{7\cdot13}=\frac{6}{91}\)

\(\frac{6}{91}\)nha

\(2\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1}{9}\)

\(\left(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{1}{9}.\frac{1}{2}\)

\(\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)

\(\frac{1}{x+1}=\frac{1}{9}-\frac{1}{18}=\frac{1}{9}\)

=>x+1=9

=>x=8

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

B = 9.10 + 10.11 + ....+ 1000.1001

Nhân B với 3 ta được:

9.10.3 + 10.11.3 + ... + 1000.1001.3 =

9.10.(11-8) + 10.11.(12-9) + .... + 1000.1001.(1002-999) =

9.10.11 – 8.9.10 + 10.11.12 – 9.10.11 + ... + 1000.1001.1002 – 999.1000.1001 =

1000.1001.1002 – 8.9.10 = 1 003 001 280

B = 1 003 001 280 : 3 = 334 333 760   

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{13\cdot14}+\frac{1}{14\cdot15}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{14}-\frac{1}{15}\)

\(=\frac{1}{2}-\frac{1}{15}\)

\(=\frac{13}{30}\)

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!

Ta có: A = 1.2 + 2.3 + 3.4 + 4.5 +....+ 98.99

⇒⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 +....+ 98.99.3

⇒⇒ 3A = 1.2.3 + 2.3(4-1) + 3.4(5-2) + 4.5(6-3) +.....+ 98.99(100-97)

⇒⇒ 3A = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 + 4.5.6 - 4.5.3 + ....+ 98.99.100 - 98.99.97

⇒⇒ 3A = 98.99.100

⇒⇒ A = 98.99.100398.99.1003 = 323400

b, tự giải nhé

 chia 3 nữa nhé thiếu

ban lam sai de bai roi nhe phan A la 1.8+8.9 sao lai la 98.99