a1=2/5,且2an-2a(n+1)=3an a(n+1)a1=2/5,且2an-2a(n+1)=3ana(n+1) 试问数列an中,任意连续两项的乘积ak*a(k+1)是否仍为an中的项,如果是,是第几项?
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a1=2/5,且2an-2a(n+1)=3an a(n+1)a1=2/5,且2an-2a(n+1)=3ana(n+1) 试问数列an中,任意连续两项的乘积ak*a(k+1)是否仍为an中的项,如果是,是第几项?
a1=2/5,且2an-2a(n+1)=3an a(n+1)
a1=2/5,且2an-2a(n+1)=3ana(n+1) 试问数列an中,任意连续两项的乘积ak*a(k+1)是否仍为an中的项,如果是,是第几项?
a1=2/5,且2an-2a(n+1)=3an a(n+1)a1=2/5,且2an-2a(n+1)=3ana(n+1) 试问数列an中,任意连续两项的乘积ak*a(k+1)是否仍为an中的项,如果是,是第几项?
[an-a(n+1)]/ana(n+1)=3/2
1/a(n+1)-1/an=3/2
1/a1=5/2
1/an是以5/2为首项,3/2为公差的等差数列.
1/an=1/a1+(n-1)*(3/2)=(3n+2)/2
an=2/(3n+2)
ak*a(k+1)
=[2/(3k+2)]*[2/(3k+5)]
=2/[(3k+2)(3k+5)/2]
=2/[3(k+2)(3k+1)/2+2]
ak*a(k+1)仍为an中的项,是第(k+2)(3k+1)/2项.
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