Question

[Trần Đức Huy]

Tính \(\frac{18}{1.2.3}+\frac{18}{2.3.4}+\frac{18}{3.4.5}+...+\frac{18}{25.26.27}\)

SP mk nha

Đây là bài thi KSCL cuối năm trường mình đấy

Answer 1

[Arima Kousei]

\(\frac{18}{1.2.3}+\frac{18}{2.3.4}+...+\frac{18}{25.26.27}\)

\(=18.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{25.26.27}\right)\)

\(=18.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{25.26}-\frac{1}{26.27}\right)\)

\(=18.\left(\frac{1}{1.2}-\frac{1}{26.27}\right)\)

\(=18.\left(\frac{1}{2}-\frac{1}{702}\right)\)

\(=18.\left(\frac{351}{702}-\frac{1}{702}\right)\)

\(=18.\frac{350}{702}\)

\(=\frac{350}{39}\)

Answer 2

[Đỗ Thanh Tùng]

=18x(1/1x2x3+1/2x3x4+1/3x4x5+...+1/25x26x27). =18x(1/1x2-1/2x3+1/2x3-1/3x4+...+1/25x26-1/26x27).                                                                 =18x(1/1x2-1/26x27).                                                =18x175/351.                                                             =350/39