已知数列an的前n项和Sn=2n^2+n,则lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]
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已知数列an的前n项和Sn=2n^2+n,则lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]的值为
Sn =2n^2+n
Sn-1=2(n-1)^2+n-1
an=Sn -Sn-1
=4n-1
lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]
=lim[1/3*1/7+1/7*1/11+1/11*1/15
=1/4lim[1/3-1/7+1/7-1/11+1/11-1/15
=1/4*1/3
=1/12
选B
再问: 1/4lim[1/3-1/7+1/7-1/11+1/11-1/15 这 步是怎么得出的
再答: 1/3*1/7=1/21=1/4*4/21=1/4*(1/3-1/7)
Sn-1=2(n-1)^2+n-1
an=Sn -Sn-1
=4n-1
lim[1/a1a2+1/a2a3+1/a3a4+...+1/anan+1]
=lim[1/3*1/7+1/7*1/11+1/11*1/15
=1/4lim[1/3-1/7+1/7-1/11+1/11-1/15
=1/4*1/3
=1/12
选B
再问: 1/4lim[1/3-1/7+1/7-1/11+1/11-1/15 这 步是怎么得出的
再答: 1/3*1/7=1/21=1/4*4/21=1/4*(1/3-1/7)
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