How can I get an exponential moving average formula from the arithmetic mean formula?

Question

Can someone explain me about stochastic gradient? If I have a recurrent formula of arithmetic mean fuctional: $$ Q_m = \frac{1}{m} \varepsilon + (1 - \frac{1}{m}) Q_{m-1} $$, where $Q_m = \frac{1}{m}\varepsilon_m + \frac{1}{m}\varepsilon_{m - 1} + ... + \frac{1}{m}\varepsilon_1$, how can I get a formula of exponential moving average: $$ Q_m = \lambda\varepsilon_m + (1 - \lambda)\lambda\varepsilon_{m-1} + (1 - \lambda)^2\lambda\varepsilon_{m-2} + (1 - \lambda)^3\lambda\varepsilon_{m-3} + ... $$, where $\lambda = \frac{1}{m}$. How can I get a second formula of $Q_m$(exponential moving average) from the first formula of $Q_m$(arithmetic mean)? Thank you in advance.