Đặt 2000 = a thì ta có
A = \(\sqrt{1+\left(a-1\right)^2+\frac{\left(a-1\right)^2}{a^2}}+\frac{a-1}{a}\)
\(=\sqrt{\frac{a^4-2a^3+3a^2-2a+1}{a^2}}+\frac{a-1}{a}\)
\(=\frac{a^2-a+1}{a}+\frac{a-1}{a}=a=2000\)
Tính giá trị:
\(P=\sqrt{1+1999^2+\frac{1999^2}{2000^2}}+\frac{1999}{2000}\)
Rút gọn A = \(\sqrt{1+1999^2+\frac{1999^2}{2000^2}}+\frac{1999}{2000}\)
tính:A=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2000\sqrt{1999}+1999\sqrt{2000}}\)
Chứng minh rằng: A=\(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{1999^2}+\frac{1}{2000^2}}\)là số hữu tỉ
Tính \(A=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
Tính
1) \(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
2) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{1998}+\sqrt{1999}}\)
Tính
N=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{1999\sqrt{1998}+1998\sqrt{1999}}\)
giúp mình với
GIẢI HỆ PHƯƠNG TRÌNH (2000 ẩn số)
\(2x_1=x_2+\frac{1}{x_2}\)(1)
\(2x_2=x_3+\frac{1}{x_3}\)(2)
\(2x_3=x_4+\frac{1}{x_4}\)(3)
..............................................................................
\(2x_{1999=x_{2000}+\frac{1}{x_{2000}}}\)(1999)
\(2x_{2000=x_1+\frac{1}{x_1}}\)(2000)
GIẢI HỆ PHƯƠNG TRÌNH (2000 ẩn số)
\(2x_1=x_2+\frac{1}{x_2}\)(1)
\(2x_2=x_3+\frac{1}{x_3}\)(2)
\(2x_3=x_4+\frac{1}{x_4}\)(3)
..............................................................................
\(2x_{1999=x_{2000}+\frac{1}{x_{2000}}}\)(1999)
\(2x_{2000=x_1+\frac{1}{x_1}}\)(2000)
