( k + 1)² - 1

To simplify \( (k + 1)^2 - 1 \), we can start by expanding \( (k + 1)^2 \):

\[ (k + 1)^2 = k^2 + 2k + 1 \]

Now, we subtract 1 from this result:

\[ (k + 1)^2 - 1 = (k^2 + 2k + 1) - 1 \]

This simplifies to:

\[ k^2 + 2k + 1 - 1 = k^2 + 2k \]

So, the final simplified expression is:

\[ k^2 + 2k \]