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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 \(n \ge 1.\)

 

 

 

please help asap

 
 Feb 12, 2021

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