# Doubt regarding improvement of State Value by n-step returns

Excerpt from Sutton and Barto:

The expected value of all $$n$$-step returns is guaranteed to improve in a certain way over the current value function as an approximation to the true value function. For any $$V$$, the expected value of the $$n$$-step return using $$V$$ is guaranteed to be a better estimate of $$V^{\pi}$$ than $$V$$ is, in a worst-state sense. That is, the worst error under the new estimate is guaranteed to be less than or equal to $$\gamma^n$$ times the worst error under $$V$$:

My question is why did they add the $$\gamma^n$$ in the RHS of the equation? My understanding is that in the LHS we use the $$E_{\pi}$$ expectation term to get the estimate of $$V^{\pi}(s)$$, then why is the difference in the second term diminished by $$\gamma^n$$. Can it be explained informally or is it a result of a proof?