( 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: \[ k^2 + 2k \]