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# help please cphill preferably or someone else

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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 $$n \ge 1.$$

Feb 12, 2021