Tính M=(1-2/6)(1-2/12)(1-2/20)….(1-2/9900) 04/08/2021 Bởi Valerie Tính M=(1-2/6)(1-2/12)(1-2/20)….(1-2/9900)
Đáp án: $M=\dfrac{101}{297}$ Giải thích các bước giải: $M=\left ( 1-\dfrac{2}{6} \right )\left ( 1-\dfrac{2}{12} \right )\left ( 1-\dfrac{2}{20} \right )…\left ( 1-\dfrac{2}{9900} \right )\\=\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}…\dfrac{9898}{9900}\\=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}…\dfrac{98.101}{99.100}\\=\dfrac{1.2.3…98}{2.3.4…99}.\dfrac{4.5.6…101}{3.4.5…100}\\=\dfrac{1}{99}.\dfrac{101}{3}\\=\dfrac{101}{297}$ Bình luận
Đáp án+Giải thích các bước giải: `M=(1-\frac{2}{6}).(1-\frac{2}{12}).(1-\frac{2}{20})…..(1-\frac{2}{9900})` `=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}…..\frac{9898}{9900}` `=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}…..\frac{98.101}{99.100}` `=\frac{(1.4).(2.5).(3.6)…..(98.101)}{(2.3).(3.4).(4.5)…..(99.100)}` `=\frac{(1.2.3…..98).(4.5.6….101)}{(2.3.4…..99)(3.4.5….100)}` `=\frac{1.101}{99.3}` `=\frac{101}{297}` Vậy `M=\frac{101}{297}` Chúc bn học tốt~~~ Bình luận
Đáp án:
$M=\dfrac{101}{297}$
Giải thích các bước giải:
$M=\left ( 1-\dfrac{2}{6} \right )\left ( 1-\dfrac{2}{12} \right )\left ( 1-\dfrac{2}{20} \right )…\left ( 1-\dfrac{2}{9900} \right )\\
=\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}…\dfrac{9898}{9900}\\
=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}…\dfrac{98.101}{99.100}\\
=\dfrac{1.2.3…98}{2.3.4…99}.\dfrac{4.5.6…101}{3.4.5…100}\\
=\dfrac{1}{99}.\dfrac{101}{3}\\
=\dfrac{101}{297}$
Đáp án+Giải thích các bước giải:
`M=(1-\frac{2}{6}).(1-\frac{2}{12}).(1-\frac{2}{20})…..(1-\frac{2}{9900})`
`=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}…..\frac{9898}{9900}`
`=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}…..\frac{98.101}{99.100}`
`=\frac{(1.4).(2.5).(3.6)…..(98.101)}{(2.3).(3.4).(4.5)…..(99.100)}`
`=\frac{(1.2.3…..98).(4.5.6….101)}{(2.3.4…..99)(3.4.5….100)}`
`=\frac{1.101}{99.3}`
`=\frac{101}{297}`
Vậy `M=\frac{101}{297}`
Chúc bn học tốt~~~