\(\frac{x+1}{97}\) + \(\frac{x+1}{98}\) - \(\frac{x+1}{99}\) - \(\frac{x+1}{100}\) \(\Leftrightarrow\) (x+1).(1/97 + 1/98 - 1/99 - 1/100) . Vì (1/97 = 1/ 98 - 1/99 - 1/100) \(\ne\) 0 \(\Rightarrow\) x+ 1= 0 \(\Leftrightarrow\) x= -1
Giải phương trình
\(\frac{x+1}{99}+\frac{x+2}{98}+\frac{x+3}{97}+\frac{x+4}{96}\)= -4
câu 1: giải hệ phương trình
\(\left(x+y\right)^2+\left(y+z\right)^4+....+\left(x+z\right)^{100}=-\left(y+z+x\right)\)
\(\left(xy\right)^2+2\left(yz\right)^4+....+100\left(zx\right)^{100}=-[\left(x+y+z\right)+2\left(yz+zx+xy\right)+......+99\left(x+y+z\right)]\)\(\left(\frac{1}{x}+\frac{1}{y}\right)^2+\left(\frac{1}{y^2}+\frac{1}{z^2}\right)^2+...+\left(\frac{1}{x^{99}}+\frac{1}{z^{99}}\right)^2=-\frac{1}{\left(xy\right)^2+2\left(yz\right)^2+.....+99\left(zx\right)^2}\)
tìm x,y,z
cho x=\(\frac{\sqrt{2}-1}{1+2}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+.............+\frac{\sqrt{100}-\sqrt{99}}{99+100}\)
chứng minh: x<1/2
Bài 1: chứng minh rằng
\(\frac{\sqrt{2}-\sqrt{1}}{2+1}\:+\frac{\sqrt{3}-\sqrt{2}}{3+2}+.\:.\:.\:+\frac{\sqrt{100}-\sqrt{99}}{100+99}< \frac{9}{20}\)
Bài 2: tìm x để \(1+\frac{3}{\sqrt{X}}\) nhỏ hơn hoặc bằng 0
\(\left(100+\frac{99}{2}+\frac{98}{3}+...+\frac{1}{100}\right):\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{101}\right)-2\)
tính
\(\left(\frac{1}{100}+\frac{99}{2}+\frac{98}{3}+...+100\right)\div\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)-2\)
Cho \(x=\frac{\sqrt{2}-1}{1+2}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+...+\frac{\sqrt{100}-\sqrt{99}}{99+100}\)
Chứng minh rằng:x<\(\frac{1}{2}\)
1) Tính tổng \(S=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
2) Giải phương trình sau : \(\left(x^2-x+1\right)^4-\left(x^2+1\right)\left(x^2-x+1\right)^2+x^2=0\)
Tính \(\left(100+\frac{99}{2}+\frac{98}{3}+...+\frac{1}{100}\right)\div\left(\frac{1}{2}+\frac{1}{3}+..+\frac{1}{101}\right)-2\)
