I am a new Latex user who's having problems when writing fractions in the \array environment. The text becomes compressed to where reading what I wrote becomes a challenge, and I have so far spent hours finding a solution to my problem with no luck. I want to the \array environment to look similar to the equations not in the \array environment.
\begin{proof}
We proceed by induction.
\begin{enumerate}
\item Let $n = 1$. Then \[ \frac{1}{1(1+1)} = \frac{1}{2} = \frac{1}{1+1} = \frac{1}{2} \]
Therefore, the base case holds.
\item Assume now by Induction that \[ \frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4} + \dotsb + \frac{1}{n(n+1)}=\frac{n}{n+1} \] holds for some $n \in{\mathbb{N}}$. We now show that \[ \frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4} + \dotsb + \frac{1}{(n+1)(n+2)}=\frac{n+1}{n+2} \] We write \[ \begin{array}{lll}
\frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3} + \dotsb + \frac{1}{(n+1)(n+2)} & = & \frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3} + \dotsb + \frac{1}{n(n+1)} + \frac{1}{(n+1)(n+2)} \\
& = & \frac{n}{n+1} + \frac{1}{(n+1)(n+2)} \\
& = & \frac{(n+1)^{2}}{(n+1)(n+2)} \\
& = & \frac{n + 1}{n + 2}.
\end{array} \]
\end{enumerate}
By Induction, \[ \frac{1}{1 \cdot 2}+ \frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4} + \dotsb + \frac{1}{(n+1)(n+2)}=\frac{n+1}{n+2} \] for every $n \in{\mathbb{N}}$.
\dfrac
(short hand for \displaystyle\frac)\[\begin{array}{lll}
with\begin{align*}
,\end{array}\]
with\end{align*}
; moreover& = &
should become&=
.\begin{array}
which is designed for matrices/arrays of values not for setting a displayed equation.\dfrac
that is usually a sign of an error elsewhere (in this case usingarray
instead ofalign*
)