\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+..+\frac{1}{7.8.9}+\frac{1}{8.9.10}\)

\(B=2\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(B=2\times\left(1-\frac{1}{10}\right)\)

\(B=2\times\frac{9}{10}\)

\(B=\frac{9}{5}\)

\(B=2\times\left(\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+\frac{1}{3\times4}-\frac{1}{4\times5}+..+\frac{1}{9\times10}\right)\)

\(B=2\times\left(\frac{1}{1\times2}-\frac{1}{9\times10}\right)\)

\(B=2\times\frac{22}{45}\)

\(B=\frac{44}{45}\)

Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+\frac{1}{4.5.6}+\frac{1}{5.6.7}+\frac{1}{6.7.8}+\frac{1}{7.8.9}+\frac{1}{8.9.10}\)

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+\frac{2}{4.5.6}+\frac{2}{5.6.7}+\frac{2}{6.7.8}+\frac{2}{7.8.9}+\frac{2}{8.9.10}\)

\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+\frac{1}{4.5}-\frac{1}{5.6}+...+\frac{1}{8.9}-\frac{1}{9.10}\)

\(2A=\frac{1}{1.2}-\frac{1}{9.10}=\frac{22}{45}\)

\(A=\frac{22}{45}:2=\frac{11}{45}\)
 

1/ 1.2.3 + 1/ 2.3.4 + 1/ 3.4.5+1/4.5.6+1/5.6.7+1/6.7.8+1/7.8.9+1/8.9.10

= 1 - 1/2 - 1/3 + 1/2 - 1/3 - 1/4 + 1/3 - 1/4 - 1/5 + 1/5 - 1/6 - 1/7 + 1/6 - 1/7 - 1/8 + 1/7 - 1/8 - 1/9 + 1/8 - 1/9 - 1/10

= 1 - 1/10 

= 9/10  

ai đồng ý voi mình thì kb nhé!

mấy người trên này toàn chép bài nhau

nhấn vào đúng 0 sẽ ra đáp án

Đặt A=11.2.3+12.3.4+....+18.9.10A=11.2.3+12.3.4+....+18.9.10

2A=21.2.3+22.3.4+....+28.9.102A=21.2.3+22.3.4+....+28.9.10

=3−11.2.3+4−22.3.4+...+10−88.9.10=3−11.2.3+4−22.3.4+...+10−88.9.10

=11.2−12.3+12.3−13.4+...+18.9−19.10=11.2−12.3+12.3−13.4+...+18.9−19.10

=11.2−19.10=2245=11.2−19.10=2245

A=1145A=1145

Ax=1145x=2245Ax=1145x=2245

x=2245:1145=2

Ta có:

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{90}\right)\)

=\(\frac{11}{45}\)

=1/2.(1/1*2-1/2*3+1/2*3-1/3*4+...+1/8*9-1/9*10)

=1/2.(1/1*2-1/9*10)

=1/2.44/90

=22/90

nha

Nghị Hoàng Vũ sai rồi kìa. 1/2.(1/2-1/90) mà bằng 11/45 à