Question

[Nguyễn Phương]

Tính:A=1/7.12+1/12.17+1/17.22+...+1/52.57

        B=10/8.13+10/13.18+10/18.23+...+10/253.258

Answer 1

[Huỳnh Quang Sang]

\(A=\frac{1}{7\cdot12}+\frac{1}{12\cdot17}+\frac{1}{17\cdot22}+...+\frac{1}{52\cdot57}\)

\(A=\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+\frac{5}{17\cdot22}+...+\frac{5}{52\cdot57}\right)\)

\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{52}-\frac{1}{57}\right)\)

\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{57}\right)=\frac{1}{5}\cdot\frac{50}{399}=\frac{10}{399}\)

\(B=\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+...+\frac{10}{253\cdot258}\)

\(B=\frac{10}{5}\left(\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+...+\frac{5}{253\cdot258}\right)\)

\(B=2\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{253}-\frac{1}{258}\right)\)

\(B=2\left(\frac{1}{8}-\frac{1}{258}\right)=2\cdot\frac{125}{1032}=\frac{125}{516}\)

Answer 2

[Huỳnh Quang Sang]

*Cái đây giải thích hơi bị " khó hiểu " :

Chỗ mẫu (12 - 7) = (17 - 12) = ... = (57 - 52) = 5

Tử là 1 , mẫu là 5 nên tử/mẫu = 1/5

Hay \(\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+...+\frac{5}{52\cdot57}\right)\)

Còn bạn Trương Bùi Linh thì :

Mẫu = (13 - 8) = (18 - 13) = (23 - 18) = ... = 5

Tử là 10,mẫu là 5 => tử / mẫu = 10/5 = 2