# Why does $\alpha=1$ mean batch MC Learning?

Here is a part of slide 4 from the link:

Why does $$\alpha=1$$ mean batch MC Learning? I do not see this clearly when I compare with averaging returns formula.
The average return formula can be reformulated: \begin{align} V_{n+1}(s) &= \frac{1}{n}\sum_{i=1}^{n}R_{i} \\ &= \frac{1}{n}\left(R_{n} +\sum_{i=1}^{n-1}R_{i} \right) \\ &= \frac{1}{n}\left(R_{n} +(n-1) \frac{1}{n-1}\sum_{i=1}^{n-1}R_{i} \right) \\ &= \frac{1}{n}\left(R_{n} + (n-1) V_{n}(s) \right) \\ &= \frac{1}{n}\left(R_{n} + nV_{n}(s) - V_{n}(s) \right) \\ &= V_{n}(s) + \frac{1}{n} (R_{n} - V_{n}(s)) \end{align} where $$V_{n}$$ is the estimate of the value function after $$n-1$$ averages over the return of the state $$s$$. We can interpret each $$i$$ as a single visit to $$s$$ or as a batch of visits of $$s$$ in which case $$R_{i}$$ would be the averaged return of this batch. Setting $$\frac{1}{n} = \alpha$$ directly results in the formula for incremental updates. Note that if we set $$n = \alpha = 1$$ we just set the value function of the state to the return of the first episode or the average of the first batch $$V(s) = R_{1}$$.