This equation from some math book,
position 1 and position 2 is in the same column, I tried
\begin{align}x_n&=\begin{aligned}[t]&\left(1 + \frac{1}{n}\right)^n = \binom{n}{0}\left(\frac{1}{n}\right)^01^n + \binom{n}{1}\left(\frac{1}{n}\right)^11^{n-1}+\binom{n}{2}\left(\frac{1} {n}\right)^21^{n-2}+\\&+\binom{n}{3}\left(\frac{1}{n}\right)^31^{n-3}+\cdots+\binom{n}{k}\left(\frac{1} {n}\right)^k1^{n-k}+\cdots+\binom{n}{n}\left(\frac{1}{n}\right)^n1^0 \end{aligned}\nonumber\\&=\begin{aligned}[t]&1 + 1 + \frac{1}{2!}\left(1 - \frac{1}{n}\right) + \frac{1}{3!}\left(1 - \frac{1} {n}\right)\left(1 - \frac{2}{n}\right) + \cdots\\&+ \frac{1}{k!}\left(1 - \frac{1}{n}\right)\cdots\left(1 - \frac{k-1} {n}\right)+\cdots+\frac{1}{n!}\left(1 - \frac{1}{n}\right)\cdots\left(1-\frac{n-1} {n}\right). \end{aligned}\end{align}but the result is not what I want.
