若数列{an},{bn}满足an×bn=1若数列{an},{bn}满足an*bn=1,an=4nˆ2-1,求{bn}的前n项和.

Question

若数列{an},{bn}满足an×bn=1
若数列{an},{bn}满足an*bn=1,an=4nˆ2-1,求{bn}的前n项和.

Answer 1

bn=1/(4n^2-1)=1/(2n+1)(2n-1)=1/2*[1/(2n-1)-1/(2n+1)]
所以Sn=1/2*[1-1/3+1/3-1/5+……+1/（2n-1)-1/(2n+1) ]消去得Sn=1/2*[1-1/(2n+1)]=n/(2n+1)
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