How can adding an infinite number of rationals yield an irrational number?

For example how come \zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}. It seems counter intuitive that you can add numbers in \mathbb{Q} and get an irrational number.


But for example \pi=3+0.1+0.04+0.001+0.0005+0.00009+0.000002+\cdots and that surely does not seem strange to you…

Source : Link , Question Author : E.O. , Answer Author : Mariano Suárez-Álvarez

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