So sánh: a)\(\frac{-3}{100}\)và \(\frac{2}{3}\) b)\(\frac{267}{-268}\)và\(\frac{-1347}{1343}\) c) \(\frac{2017\times2018-1}{2017\times2018}\)và\(\frac{2018\times2019-1}{2018\times2019}\) e)\(\frac{2017\times2018}{2017\times2018+1}\)và\(\frac{2018\times2019}{2018\times2019+1}\) Gải cách rút gọn cám ơn ạ
So sánh:\(2017\times2018\times2019\)với\(2018^3\)
Đặt 2018=a
\(VT=a\left(a-1\right)\left(a+1\right)=a\left(a^2-1\right)=a^3-a< a^3\)
Do đó: VT<VP
so sán a và b biết a=\(\frac{2017\times2018-1}{2017\times2018}\)và b =\(\frac{2019\times2020-1}{2019\times2020}\)
\(Ta\)có :\(a\)=\(\frac{2017\cdot2018-1}{2017.2018}\)=\(\frac{2017.2018}{2017.2018}\)-\(\frac{1}{2017.2018}\)=1-\(\frac{1}{2017.2018}\)
\(b\)=\(\frac{2019.2020-1}{2019.2020}\)=\(\frac{2019.2020}{2019.2020}\)-\(\frac{1}{2019.2020}\)=1-\(\frac{1}{2019.2020}\)
Vì \(\frac{1}{2018.2019}\)> \(\frac{1}{2019.2020}\)nên \(a\)< \(b\)(sử dụng phần bù)
Tính nhanh:
a)\(\frac{131313}{151515}+ \frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
b)\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2017\times2018}\)
c)\(\frac{1}{3\times5}+\frac{1}{4\times7}+\frac{1}{7\times9}+...\frac{1}{2015\times2017}+\frac{1}{2017\times2018}\)
\(a,\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{7.9}\right)\)
\(=13\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(=13.\frac{2}{9}=\frac{26}{9}\)
\(b,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}=\frac{2017}{2018}\)
P/s :Dấu chấm là dấu nhân nha
\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13.10101}{15.10101}+\frac{13.10101}{35.10101}+\frac{13.10101}{63.10101}+\frac{13.10101}{99.10101}\)
\(=13.\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=\frac{13}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{11}{33}-\frac{3}{33}\right)\)
\(=\frac{13}{2}.\frac{8}{33}\)
\(=\frac{52}{33}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}\)
\(=\frac{2017}{2018}\)
Sửa đề chút:
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}+\frac{1}{2017.2018}\)
\(=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2015.2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
B tự làm nốt nhé
Tính nhanh : \(\frac{2018\times2017-1}{2016\times2018+2017}\)
\(\frac{2018\times2017-1}{2016\times2018+2017}\)
\(=\frac{2018\times\left(2016+1\right)-1}{2016\times2018+2017}\)
\(=\frac{2018\times2016+2018-1}{2016\times2018+2017}\)
\(=\frac{2018\times2016+2017}{2016\times2018+2017}\)
\(=1\)
Tính nhanh:( giúp mik với )
a) \(2018^2-2017\times2019\)
b) \(\frac{2018^3+1}{2018-2017}\)
2017.2019 = (2018-1)(2018+1) = 20182 -1 => a =1
b= 20183 +1 (???)
Ai giup minh cau nay voi
B=\(\frac{1}{1\times2}\)+\(\frac{1}{2\times3}\)+\(\frac{1}{3\times4}\)+...+\(\frac{1}{2017\times2018}\)
\(B=\frac{1}{1.2}=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(B=\left(1-\frac{1}{2018}\right)-\left(\frac{1}{2}-\frac{1}{2}\right)-...-\left(\frac{1}{2017}-\frac{1}{2017}\right)\)
\(B=1-\frac{1}{2018}=\frac{2017}{2018}\)
Vậy \(B=\frac{2017}{2018}\)
so sánh 2 số A và B nếu
\(A=-\frac{1}{2018}-\frac{3}{2017^2}-\frac{5}{2017^3}-\frac{7}{2017^4};B=\frac{-1}{2018}-\frac{7}{2017^2}-\frac{5}{2017^3}-\frac{3}{2017^4}\)
Tính gía trị của biểu thức
\(\frac{\left(2015^2\times2025+31\times2016-1\right)\times\left(2015\times2020+4\right)}{2016^2\times2017\times2018\times2019\times2020}\)
