已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=an*a(n+1)求数列bn的前n项和sn
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已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=an*a(n+1)求数列bn的前n项和sn已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=a
已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=an*a(n+1)求数列bn的前n项和sn
已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=an*a(n+1)求数列bn的前n项和sn
已知数列an满足a1=1,an=(an-1)/(3a(n-1)+1),设bn=an*a(n+1)求数列bn的前n项和sn
an=a/(3a+1),
∴1/an=3+1/a=……=3(n-1)+1/a1=3n-2,
∴an=1/(3n-2),
∴bn=an*a=1/[(3n-2)(3n+1)]=(1/3)[1/(3n-2)-1/(3n+1)],
∴数列{bn}的前n项和Sn=(1/3)[1-1/4+1/4-1/7+……+1/(3n-2)-1/(3n+1)]
=(1/3)[1-1/(3n+1)]
=n/(3n+1).
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