Question: What is a better way of saying "in order to demonstrate this, I will..."? I already use "to that effect" in the same paragraph. I'm looking for something as compact and concise as "to that effect" that will also be a good transition for the beginning of a new paragraph.

Answer: 
Perhaps "To illustrate this, I will...", "Demonstrating this, I will..." or "As an example,.."
"I'll show this (is true, is so, isn't so) by. . .