# What is the correct ascending order here?

What is the correct increasing order here:

$$\alpha=\dfrac{1^{78}+2^{78}+3^{78}+...+78^{78}}{78}, \beta=\dfrac{1^{78}+3^{78}+5^{78}+...+77^{78}}{39}, \gamma=\dfrac{2^{78}+4^{78}+6^{78}+...+78^{78}}{39}$$

I tried evaluating the numbers one-by-one, but that seems a difficult and unsophisticated manner.

Note that $$\beta<\gamma$$. Also, note that $$\alpha$$ is the arithmetic mean of $$\beta$$ and $$\gamma$$. Thus,
$$\beta<\alpha<\gamma$$