Đáp án:
Giải thích các bước giải:
a) ` 1/20.23 + 1/23 . 26 + 1/26.29 +...+ 1/77.80 < 1/9`
`= 1.( 1/20 - 1/23 + 1/23 - 1/26 + 1/26 - 1/29 +... + 1/77 - 1/80 ) < 1/9`
`= 1.(1/20 - 1/80) < 1/9`
`=1.3/80 < 1/9`
`= 3/80 < 1/9`
DO ` 3/80 < 1/9`
`=> 1/20.23 + 1/23 . 26 + 1/26.29 +...+ 1/77.80 < 1/9`
`B)` Gọi ` ƯCLN(7n+4;5n+3)` là `d`
ta có :\(\left[ \begin{array}{l}7n+4 \vdots d\\5n+3 \vdots d\end{array} \right.\)
\(\left[ \begin{array}{l}5(7n+4) \vdots d\\7(5n+3) \vdots d\end{array} \right.\)
\(\left[ \begin{array}{l}35n+20 \vdots d\\35n+21 \vdots d\end{array} \right.\)
`( 35n + 20 - 35n+21 ) \vdots d `
` -1 \vdots d `
`d \inƯ(-1)={1;-1}`
`D = 1;-1`
vậy ps`(7n+4)/(5n+3)` là ps tối giản
