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I can't seem to see what is happening to make this equivalence. More specifically, how the left-side's $n+1$ makes it into the right side's numerator. $$ \frac {n(n+1)} 2 + (n+1) = \frac {(n+1)(n+2)}2 $$

Battle J. Butts
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    Notice that

    $$\frac{n(n+1)}{2} + n+1 = \frac{n(n+1)}{2} + \frac{2(n+1)}{2}$$

    Then you can factor $n+1$ out.

     – user0102 Mar 13 '21 at 21:37

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hint: Factor the $(n+1)$ using distributive property, and note also that $\dfrac{n}{2}+1 = \dfrac{n+2}{2}$