How to write out the full series from its sum!


Sometimes you'll be given a sum in summation notation, and asked to expand the sum into a sum of individual terms.

What this really means is that you're going to look at the index, which is where the sum begins and ends, and then plug all of those values into the function, adding each value to the next, to create an expanded sum. Really all you're doing here is listing out the terms of the sum, instead of having them consolidated into one sum.

The expanded sum will represent exactly the same thing as the summation notation that you started with.

Want to learn more about error bounds and integrals? I have a step-by-step course for that. 😃