I need help with the following proof:
Let $\displaystyle (x_{n})_{n}$ be a sequence of real numbers such that $\displaystyle x_{n} + x_{n+1}$ converges and $\displaystyle x_{n}x_{n+1}$ converges. Show that $\displaystyle (x_{2n}) $converges
I need help with the following proof:
Let $\displaystyle (x_{n})_{n}$ be a sequence of real numbers such that $\displaystyle x_{n} + x_{n+1}$ converges and $\displaystyle x_{n}x_{n+1}$ converges. Show that $\displaystyle (x_{2n}) $converges