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Mathematics, 16.05.2021 18:10 ginger1234
Please help, I have no idea how to do it!
The sequence $(a_n)$ is defined by $a_1 = \frac{1}{2}$ and
\[a_n = a_{n - 1}^2 + a_{n - 1}\]for $n \ge 2.$
Prove that
\[\frac{1}{a_1 + 1} + \frac{1}{a_2 + 1} + \dots + \frac{1}{a_n + 1} < 2\]for all $n \ge 1.$
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