Step 1

$\hat{f}(x) \leftarrow \hat{f}(x)+\lambda \hat{f}^b(x).$

Step 2

$r_i \leftarrow r_i - \lambda \hat{f}^b(x_i).$

Final step

$\hat{f}(x) = \sum_{b=1}^B \lambda \hat{f}^b(x).$

How does this formula explain the gradient boosting algorithm or could somebody shortly explain how the gradient boosting algorithm works in terms of math.