Sửa đề: \(M=\sqrt{1^2+2017^2+\dfrac{2017^2}{2018^2}}+\dfrac{2017}{2018}\)
\(=\sqrt{1^2+\dfrac{1}{\left(\dfrac{1}{2017}\right)^2}+\dfrac{1}{\left(-\dfrac{2018}{2017}\right)^2}}+\dfrac{2017}{2018}\)
\(=\sqrt{\left(\dfrac{1}{1}+\dfrac{1}{\dfrac{1}{2017}}+\dfrac{1}{-\dfrac{2018}{2017}}\right)^2}+\dfrac{2017}{2018}\)
\(=1+2017-\dfrac{2017}{2018}+\dfrac{2017}{2018}\)
=2018
\(\sqrt{1+2017^2+\dfrac{2017^2}{2018^2}}+\dfrac{2017}{2018}\)
\(\sqrt{1+2017^2+\dfrac{2017^2}{2018^2}}+\dfrac{2017}{2018}\)
a) \(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+....+\dfrac{1}{\sqrt{19}+\sqrt{20}}\)
b) \(\sqrt{1+2017^2+\dfrac{2017^2}{2018^2}}+\dfrac{2017}{2018}\)
Tính :
\(\dfrac{1}{1+\sqrt{2}}+\dfrac{1}{\sqrt{2}+3}+.....+\dfrac{1}{\sqrt{2017}+2018}\)
Rút gọn
A=\(\sqrt{1^2+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1^2+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+......+\sqrt{1^2+\dfrac{1}{2017^2}+\dfrac{1}{2018^2}}\)
HELP ME,PLS
Không sử dụng máy tính hãy so sánh : A=\(\frac{2017}{\sqrt{2018}}+\frac{2018}{\sqrt{2017}}\) và B=\(\sqrt{2017}+\sqrt{2018}\)
Tính giá trị của biểu thức \(P=\dfrac{4\left(x+1\right)x^{2018}-2x^{2017}+2x+1}{2x^2+3x}\) tại \(x=\sqrt{\dfrac{1}{2\sqrt{3}-2}-\dfrac{3}{2\sqrt{3}+2}}\)
Cho ba số thực dương x, y, z thỏa mãn: xy+yz+zx=2017. chứng minh : \(\sqrt{\dfrac{yz}{x^2+2017}}+\sqrt{\dfrac{zx}{y^2+2017}}+\sqrt{\dfrac{xy}{z^2+2017}}\le\dfrac{3}{2}\)
cau a cho x,y,z\(\ne\)0 thoa man x+y+z=0. CM: \(\sqrt{\dfrac{1}{x^2}+\dfrac{1}{y^2}+\dfrac{1}{z^2}}=|\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}|\) cau b tinh G=\(\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+\sqrt{1+\dfrac{1}{4^2}+\dfrac{1}{5^2}}+.....+\sqrt{1+\dfrac{1}{2017^2}+\dfrac{1}{2018^2}}\)
