feat: add more desc for tests

cheatsheets/ma1521/finals.tex

@@ -399,10 +399,12 @@
        $n^{th}$ term & $\lim\limits_{n \to \infty} a_{n} \ne 0$ or does not exist, then divergent \\\hline
        Integral & $f(n)=a_{n}$ is continuous, positive, decreasing function $\forall x\geq 1$ and $\int_{1}^{\infty}f(x)dx$ converges else divergent \\\hline
        p-series & $\sum_{n=1}^{\infty} \frac{1}{n^{p}}$convergent $\leftrightarrow p > 1$ \\\hline
-       Ratio & $0 \geq \lim\limits_{n \to \infty} |\frac{a_{n+1}}{a_{n}}|=L < 1$ abs. convergent, $> 1$ divergent, $= 1$ inconclusive \\\hline
-       Root & $0 \geq \lim\limits_{n \to \infty} \sqrt[n]{a_{n}}=L < 1$ abs. convergent, $> 1$ divergent, $= 1$ inconclusive \\\hline
+       Harmonic Series & $\sum_{n=1}^{\infty} \frac{1}{n}$ divergent \\\hline
+       Ratio \tiny{If Factorial} & $0 \geq \lim\limits_{n \to \infty} |\frac{a_{n+1}}{a_{n}}|=L < 1$ abs. convergent, $> 1$ divergent, $= 1$ inconclusive \\\hline
+       Root \tiny{If nth power} & $0 \geq \lim\limits_{n \to \infty} \sqrt[n]{a_{n}}=L < 1$ abs. convergent, $> 1$ divergent, $= 1$ inconclusive \\\hline
        Alternating series & $b_{n}$ decreasing, $\lim\limits_{n \to \infty}b_{n} = 0$, then $\sum_{n=1}^{\infty}(-1)^{n-1}b_{n} = b_{1}-b_{2}+b_{3}... $ is convergent \\\hline
        Power Series & $b_{n}$ decreasing, $\lim\limits_{n \to \infty}b_{n} = 0$, then $\sum_{n=1}^{\infty}(-1)^{n-1}b_{n} = b_{1}-b_{2}+b_{3}... $ is convergent \\\hline
+       Comparison Test & Compare to well known series such as p-series, harmonic \\\hline
      \end{tabular}
  \end{center}
 
@@ -445,6 +447,5 @@ For $-1 < x < 1$
         \\   & $= 1 + kx + \frac{k(k-1)}{2!}x^2 + \dots$
 \end{tabular}
 
-
 \end{multicols*}
 \end{document}