Question

Problema 75 , Multumesc !

Answer 1

[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]