Question

\(\frac{6}{2x5}+\frac{6}{5x8}+\frac{6}{8x11}+.......+\frac{6}{98x101}\)

Answer 1

Đặt \(Shin=\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{98.101}\)

\(\Rightarrow3Shin=\frac{6}{2}-\frac{6}{5}+\frac{6}{5}-\frac{6}{8}+\frac{6}{8}-\frac{6}{11}+...+\frac{6}{98}-\frac{6}{101}\)

\(\Leftrightarrow3Shin=\frac{6}{2}-\frac{6}{101}=\frac{297}{101}\)

N/t: . là dấu nhân nha! Cái đó lớp 5 chưa biết đâu! Lên cấp 2 mới học. Trong bài làm bạn cứ ghi là dấu  " x"  thay cho dấu "." của mình nha!

Answer 2

Đặt A = 6/2.5 + 6/5.8 + ... + 6/98.101

=> A = 6.(1/2.5 + 1/5.8 + ... + 1/98.101)

=> 3A = 6.(3/2.5 + 3/5.8 + ... + 3/98.101)

=> 3A = 6.(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/98 - 1/101)

=> 3A = 6.99/202

=> 3A = 297/101

=> A = 99/101

Answer 3

x là nhân hả

\(\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{98.101}\)

\(=2\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+......+\frac{3}{98.101}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{98}-\frac{1}{101}\right)\)

\(=2\left(\frac{1}{2}+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{8}+\frac{1}{8}\right)+....+\left(\frac{-1}{98}+\frac{1}{98}\right)-\frac{1}{101}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{101}\right)\)

\(=2.\frac{99}{202}\)

\(=\frac{99}{101}\)

Answer 4

Ta có:

\(\frac{6}{2\times5}+\frac{6}{5\times8}+\frac{6}{8\times11}+.....+\frac{6}{98\times101}\)

\(=2\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+....+\frac{3}{98\times101}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{98}-\frac{1}{101}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{101}\right)\)

\(=2\times\frac{98}{2\times101}\)

\(=\frac{98}{101}\)