Question

Tính hợp lí

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

Answer 1

ta có:1/1.2-1/2.3+1/2.3-1/3.4+.....+1/8.9-1/9.10

       =1/1.2-1/9.10=1/2-1/90 

       =45/90-1/90=44/90=22/45

Duyệt nha

Answer 2

tk minh 

mk khac tk cho !

Answer 3

Đặt A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\)

=> 4A = \(\frac{4}{1.2.3}+\frac{4}{2.3.4}+...+\frac{4}{8.9.10}\)

=> 4A = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\)

=> 4A = \(\frac{\text{1}}{\text{1}.2}-\frac{\text{1}}{9.\text{1}0}\)

=> 4A = \(\frac{\text{1}}{2}-\frac{\text{1}}{90}=\frac{22}{45}\)

=> A = \(\frac{\text{1}\text{1}}{90}\)

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