Consider the sequence defined: $a_1=0, a_{n+1}=3+\sqrt{11+a_n}$, show that is bounded above and increasing using induction.

real-analysis sequences-and-series

Solution 1:

This was answered in the comments 10 months ago. Looks good, but André offered advice for clarifying part (b).

A minor point: You find using your method that the limit $L$ is a solution to the quadratic equation $x^2-7x-2$. One of the solutions to this equation is positive, and the other is negative, and you can deduce that the limit is the positive solution.

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