Câu 1. Tính hợp lý giá trị các biểu thức sau :
a. A = ( 689 - 31 ) - ( 269 - 131 )
b. B = \(\left(\frac{1}{2}+\frac{2016}{2017}+\frac{2017}{2018}+1\right)\times\left(\frac{2016}{2017}+\frac{2017}{2018}+\frac{3}{4}\right)-\left(\frac{1}{2}+\frac{2016}{2017}+\frac{2017}{2018}\right)\times\left(\frac{2016}{2017}+\frac{2017}{2018}+\frac{3}{4}+1\right)\)c. C = \(1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
1. \(B=\frac{12}{\left(2.4\right)^2}+\frac{20}{\left(4.6\right)^2}+...+\frac{388}{\left(96.98\right)^2}+\frac{396}{\left(98.100\right)^2}\)
So sánh \(B\) với \(\frac{1}{4}\)
2. SO sánh \(A=\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}\) và \(B=\frac{2015+2016+2017}{2016+2017+2018}\)
Tính
\(\left(\frac{1}{4}-\frac{1}{5}-\frac{1}{20}\right)\left(\frac{2017}{2018}-\frac{2018}{2019}\right)\)
\(\left(2018^{2017}\times2017^{2018}\right)\left(0^{2018}\times2981\right)\)
1. Cho A=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)và B=\(\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2017}+\frac{1}{2018}\)Tính \(\left(\frac{A}{B}\right)^{2018}\)
2. Tìm x biết
a)\(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{x.\left(x+2\right)}=\frac{20}{41}\)
b)\(|x+2016|+|x+2017|+2018=3x\)
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}\right).x+2017=\frac{2018}{1}+\frac{2018}{2}+\frac{2020}{3}\). Tìm x
So sanh :\(\frac{2017}{2018}+\frac{2018}{2019}va\frac{2015}{2016}+\frac{2016}{2017}\)
cho \(x,y\ne0\)thỏa mãn\(x^{2015}+x^{2015}=x^{2016}+x^{2016}=x^{2017}+x^{2017}\)
tính \(S=2018.\left(x^{2018}+y^{2018}\right)\)
Tìm x biết
a) \(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2019}\right).x=\frac{2018}{1}+\frac{2017}{2}+\frac{2016}{3}+...+\frac{2}{2017}+\frac{1}{2018}\)
b) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2017}{2019}\)