若等比数列前n项,前2n项,前3n项的和分别为sn s2n s3n 求证sn∧2+s2n∧2=sn(s2n+s3n)
问题描述：
若等比数列前n项,前2n项,前3n项的和分别为sn s2n s3n 求证sn∧2+s2n∧2=sn(s2n+s3n)
答
an = a1q^(n-1)Sn = a1(q^n-1)/(q-1)(Sn)^2 + (S(2n))^2= [a1(q^n-1)/(q-1)]^2 +[a1(q^(2n)-1)/(q-1)]^2= [a1/(q-1)]^2 .[ q^(4n) -q^(2n) - 2q^n + 2]Sn[S(2n) + S(3n) ]=[a1(q^n-1)/(q-1)] .[ a1(q^(2n)-1)/(q-1) ...