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/(

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]

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