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**ulysses123** Prove that:

$\displaystyle lim_m$$\displaystyle _\rightarrow$$\displaystyle _\infty $ $\displaystyle \mid $$\displaystyle \frac{B_{2m}}{2m}$$\displaystyle \mid$$\displaystyle =$$\displaystyle \infty$

Exploit the fact that the zeta function:

$\displaystyle \zeta(2m)$$\displaystyle <$$\displaystyle 1$

and $\displaystyle (2m) $ $\displaystyle ! $ $\displaystyle >$$\displaystyle \frac{(2m)^{2m}}{e^{2m}}$

I have to use the formula relating the zeta function to $\displaystyle B_{2m}$ to prove this, but i cannot show that it is equal to infinity