Mathematical Methods in the Physical Sciences/Chapter 1/Section 2
Contents
Overview
This is a notation chapter. You're simply becoming more familiar with the terminology and notation of infinite series.
The <math>\sum</math> symbol may be new. Well, it's no longer new after this chapter. Get used to it. It is going to be your best friend for a long time.
Problems
1
2
The <math>(-1)^n</math> is the secret sauce for how to get alternating terms. Be careful: if the 1st term is positive, then you need <math>-1(-1)^n</math> or <math>(-1)^{n+1}</math>.
3
4
5
6
7
8
When you have consecutive multiplied numbers, then factorials could be involved.
Note that <math>5!/3!</math> is simply <math>5 \cdot 4</math>. The 3, 2, 1 terms disappear by dividing by <math>3!</math>.
Of course, you can always do <math>(n+1)(n)(n-1)</math> or something similar, but I think factorials are cooler.
