[tex](b_1^2+b_2^2+...+b_n^2)(b_2^2+b_3^2+...+b_{n+1}^2)=\\
=b_1^2(1+q^2+...+q^{2(n-1)})\cdot b_1^2(q^2+q^3+...+q^{2n})=\\
=(b_1^2)^2\cdot q^2(1+q^2+...+q^{2(n-1)})^2=\\
= [(b_1^2)\cdot q(1+q^2+...+q^{2(n-1)})]^2=\\
= [b_1\cdot b_1q\cdot(1+q^2+...+q^{2(n-1)})]^2=\\
=[b_1\cdot b_2\cdot(1+q^2+...+q^{2(n-1)})]^2=\\
=(b_1b_2+b_1q\cdot b_2q+...+b_1q^{n-1}\cdot b_2q^{n-1})^2=\\
=(b_1b_2+b{_2b_3+...+b_nb_{n+1})^2
[/tex]
