It is known $\sum_{n = n_0} ^\infty \frac{1}{n^2}$ converges. It is also easy to see if $n_0$ increases, the tail of the sum decreases. How fast does this decay happen? In other words, is there an inequality stating something like $$ \sum_{n = n_0} ^\infty \frac{1}{n^2} \leq \frac{C}{n_0} $$ with $C > 0$ being some constant independent of $n_0$?
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