〔1+(-1)ˇ2n-2/(2n-1)〕×〔1+(-1)ˇ2n-1/2n〕
=〔1+1/(2n-1)〕×〔1-1/2n〕
=2n/(2n-1)×(2n-1)/2n
=1
∴An=
1/(n+1)-〔1+(-1/2)〕×〔1+(-1)ˇ2/3〕×〔1+(-1)ˇ3/4〕…〔1+(-1)ˇ2n-1/2n〕
=1/(n+1)-〔1+(-1/2)〕
=1/(n+1)-1/2
An+1=1/(n+2)-1/2
∴An>An+1
A10最大
〔1+(-1)ˇ2n-2/(2n-1)〕×〔1+(-1)ˇ2n-1/2n〕
=〔1+1/(2n-1)〕×〔1-1/2n〕
=2n/(2n-1)×(2n-1)/2n
=1
∴An=
1/(n+1)-〔1+(-1/2)〕×〔1+(-1)ˇ2/3〕×〔1+(-1)ˇ3/4〕…〔1+(-1)ˇ2n-1/2n〕
=1/(n+1)-〔1+(-1/2)〕
=1/(n+1)-1/2
An+1=1/(n+2)-1/2
∴An>An+1
A10最大