设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3S(n+2)(n=1,2,3) 设bn=2,S(n+1)=3S(n+2)(n=1,2,3.)注:n+1和n+2为下标求证;设bn=an/(Sn平方),求证b1+b2+b3.bn
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![设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3S(n+2)(n=1,2,3) 设bn=2,S(n+1)=3S(n+2)(n=1,2,3.)注:n+1和n+2为下标求证;设bn=an/(Sn平方),求证b1+b2+b3.bn](/uploads/image/z/5090255-71-5.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94%E6%BB%A1%E8%B6%B3S1%3D2%2CS%28n%2B1%29%3D3S%EF%BC%88n%2B2%EF%BC%89%28n%3D1%2C2%2C3%29+%E8%AE%BEbn%3D2%2CS%28n%2B1%29%3D3S%EF%BC%88n%2B2%EF%BC%89%28n%3D1%2C2%2C3.%29%E6%B3%A8%EF%BC%9An%2B1%E5%92%8Cn%2B2%E4%B8%BA%E4%B8%8B%E6%A0%87%E6%B1%82%E8%AF%81%3B%E8%AE%BEbn%3Dan%2F%EF%BC%88Sn%E5%B9%B3%E6%96%B9%EF%BC%89%2C%E6%B1%82%E8%AF%81b1%2Bb2%2Bb3.bn)
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3S(n+2)(n=1,2,3) 设bn=2,S(n+1)=3S(n+2)(n=1,2,3.)注:n+1和n+2为下标求证;设bn=an/(Sn平方),求证b1+b2+b3.bn
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3S(n+2)(n=1,2,3) 设bn=2,S(n+1)=3S(n+2)(n=1,2,3.)
注:n+1和n+2为下标
求证;设bn=an/(Sn平方),求证b1+b2+b3.bn
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3S(n+2)(n=1,2,3) 设bn=2,S(n+1)=3S(n+2)(n=1,2,3.)注:n+1和n+2为下标求证;设bn=an/(Sn平方),求证b1+b2+b3.bn
S(n+1)=3S(n+2)
S(n+2)/(S(n+1)=1/3 S1=2
Sn=S1q的(n-1)次方
=2x(1/3)的(n-1)次方
S(n-1)=2x(1/3)的(n-2)次方
an=Sn-S(n-1)
=2x(1/3)的(n-1)次方-2x(1/3)的(n-2)次方
=2[(1/3)的(n-1)次方-(1/3)的(n-2)次方]
bn=an/(Sn平方)
=2[(1/3)的(n-1)次方-(1/3)的(n-2)次方]/[2x(1/3)的(n-1)次方]²
=2(1/3)的(n-1)次方/[2x(1/3)的(n-1)次方]²-2(1/3)的(n-2)次方/[2x(1/3)的(n-1)次方]²
=1/[2x(1/3)的(n-1)次方]-3/[2x(1/3)的(n-1)次方]
=-2/[2x(1/3)的(n-1)次方]
b1+b2+b3.bn
=-2/[2x(1/3)的0次方]-2/[2x(1/3)的1次方]-2/[2x(1/3)的2次方].-2/[2x(1/3)的(n-1)次方]
=-1/(1/3)的0次方-1/(1/3)的1次方-1/(1/3)的2次方.-1/(1/3)的(n-1)次方
=-[1/(1/3)的0次方+1/(1/3)的1次方+1/(1/3)的2次方+.+1/(1/3)的(n-1)次方]
=-[3的0次方+3的1次方+3的2次方+.+3的(n-1)次方]