a=√2006-√2005,b=√2007-√2006,c=√2008-√2007 怎样比较这3个数的大小

a=√2006-√2005,b=√2007-√2006,c=√2008-√2007 怎样比较这3个数的大小
a=√2006-√2005,b=√2007-√2006,c=√2008-√2007 怎样比较这3个数的大小

a=√2006-√2005,b=√2007-√2006,c=√2008-√2007 怎样比较这3个数的大小
a=√2006-√2005
=1/(√2006+√2005),
b=√2007-√2006
=1/(√2007+√2006),
c=√2008-√2007
=1/(√2008+√2007 )
分母大的反而小
所以
a>b>c

a的倒数是√2006+√2005
b的倒数是√2006+√2006
c的倒数是√2008+√2007
所以a>b>c