i had this problem in my book that i wasn't able to do. I kinda had the idea of what it involved but just wanted to clear it up with you guys. So the problem is: Suppose that an ->L and bn ->L. Show that a1,b1,a2,b2,... converges to L. So here it seems to me like i can obviously define a new sequence cn, like that in the pinching theorem. But using other definitions(epsilon, etc.) of sequences, how do i come up with a proof of this.