\(\left(\frac{2006-2005}{2006+2005}\right)^2=\frac{2006^2-2005^2}{2006^2+2005^2}.\)
Vì \(\frac{2006^2-2005^2}{2006^2+2005^2}=\frac{2006^2+2005^2}{2006^2+2005^2}\)nên => \(\left(\frac{2006-2005}{2006+2005}\right)^2=\frac{2006^2-2005^2}{2006^2+2005^2}.\)
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
\(\frac{a+2006}{a-2006}=\frac{b+2005}{b-2005}chứngminh\frac{a}{b}=\frac{2006}{2005}\)
a=\(\frac{2005^{2005}+1}{2005^{2006}+1}\) va b=\(\frac{2005^{2004}+1}{2005^{2005}+1}\)
so sánh a và b
C=\(\frac{\frac{2006}{2}}{\frac{2006}{1}}\) +\(\frac{2006}{\frac{3}{\frac{2005}{2}}}\) +\(\frac{2006}{\frac{4}{\frac{2004}{3}}}\) +...+\(\frac{2006}{\frac{2007}{\frac{1}{2006}}}\)
so sánh \(\sqrt{2005+2006}và\sqrt{2005}+\sqrt{2006}\)
Cho x = 2005. Tính giá trị của biểu thức:
\(x^{2005}-2006.x^{2004}+2006.x^{2003}-2006.x^{2002}+...-2006.x^2+2006x-1\)
Tính:
S = \(\frac{2}{2005+1}\)+ \(\frac{2^2}{2005^2+1}\)+ \(\frac{2^3}{2005^{2^2}+1}\)+ \(\frac{2^4}{2005^{2^3}+1}\)+ ...+ \(\frac{2^{n+1}}{2005^{2^n}+1}\)+ ...+ \(\frac{2^{2006}}{2005^{2^{2005}}+1}\)
Tính: S
S= \(\frac{2}{2005+1}\) + \(\frac{2^2}{2005^2+1}\)+ \(\frac{2^3}{2005^{2^2}+1}\)+ \(\frac{2^4}{2005^{2^3}+1}\)+ .... + \(\frac{2005^{2006}}{2005^{2^{2005}}+1}\)+ .... + \(\frac{2^{n+1}}{2005^{2^n}+1}\)
So sánh M=15^2007+10/15^2006+10 và N = 15^2006+10/15^2005+10
