60

duyệt đi

Gọi ƯCLN( 12n+1; 30n+2 ) = d

⇒ 12n+1 ⋮ d ⇒ 5.( 12n+1 ) ⋮ d

⇒ 30n+2 ⋮ d ⇒ 2.( 30n+2 ) ⋮ d

⇒ [2.( 30n+2 ) -  5.( 12n+1 ) ] ⋮ d

⇒ [ ( 60n+4 ) - ( 60n+5 ) ] ⋮ d

⇒ - 1 ⋮ d ⇒ d = + 1

Vì ƯC( 12n+1; 30n+2 ) = + 1 ⇒ \(\frac{12n+1}{30n+2}\) là p/s tối giản ( đpcm )

Đặt tính theo cột dọc

\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}\)

\(=1-\left(\frac{1}{4}-\frac{1}{4}\right)-\left(\frac{1}{7}-\frac{1}{7}\right)-\left(\frac{1}{10}-\frac{1}{10}\right)-...-\left(\frac{1}{40}-\frac{1}{40}\right)-\frac{1}{43}\)

\(=1-\frac{1}{43}=\frac{42}{43}\)

cay đắng trong lòng