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If we have $x_i=1$ then $$\sum_{i=0}^\infty x_i=+\infty\,.\eqno(1a)$$

We further have:
 $${x^3\over 3}=\int_0^x t^2\,dt\eqno(1b)$$
and for suitable $a_i$ even
  $$\sqrt{x+1}=\sum_0^\infty a_i\,.\eqno(2)$$
This concludes the sample.
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