数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =

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数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =

数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =
数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =

数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =

n≥2时,
[a(n-1)-an]/[ana(n-1)]=[an-a(n+1)]/[ana(n+1)]
1/an -1/a(n-1)=1/a(n+1)-1/an
数列{1/an}是等差数列.
1/a1=1/2
1/a2-1/a1=1/1-1/2=1/2
数列{1/an}是以1/2为首项,1/2为公差的等差数列.
1/an =1/2 +(1/2)(n-1)=n/2
an=2/n
a100=2/100=1/50

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