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\(\displaystyle \sum_{x=1}^{\infty}\frac{1}{x}\) diverges.

But \(\displaystyle \sum_{x=1}^{\infty}\frac{1}{x^{2}}=\frac{\pi^{2}}{6}\)

How can we prove that \(\displaystyle \sum_{x=1}^{\infty}\left(\frac{1}{x^{\left(1+epsilon\right)}}\right)\) converges to a finite value?

Thanks in advance.

Bincy.