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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.

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

$$\beta<\alpha<\gamma$$

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