数列{an}满足a1=3/2,an+1=an2-an+1,求证：1/an=1/(an)-1 - 1/(an+1)-1 设Sn=1/a1+1/a2+...+1/an,n>2数列{an}满足a1=3/2,an+1=an2-an+1,求证：1/an=1/(an)-1 - 1/(an+1)-1设Sn=1/a1+1/a2+...+1/an,n>2证明1

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第一问好正
需支出数列单调增大于0
第二问
根据第一问结论
sn=1/a1+1/a2-1 -1/a3-1+.+1/an-1 -1-1/an-1
=1/a1+1/a2-1-1/an-1
=2-1/an-1
an单增
-1/an-1 单增 （-1/a3-1,2）