In Stochastic Gradient Descent $($SGD$)$ with batch size and momentum $,$ the step taken at time is:

where is the batch gradient and is the gradient of the $-$th data$-$point. Let's now expand the recursion of momentum

If we assume that the gradients do not change significantly from one SGD step to the next, we can further simplify this expression to

One final simplification is to remove the rounding due to the batching