Question
In Exercises $91-98$ , assume that each sequence converges and find itslimit.$$\begin{array}{l}{\sqrt{1}, \sqrt{1+\sqrt{1}}, \sqrt{1+\sqrt{1+\sqrt{1}}}} \\ {\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1}}}}, \ldots}\end{array}$$
Step 1
The sequence is defined as follows: $a_1 = \sqrt{1}$, $a_2 = \sqrt{1+\sqrt{1}}$, $a_3 = \sqrt{1+\sqrt{1+\sqrt{1}}}$, and so on. We can see that each term in the sequence is the square root of 1 plus the previous term in the sequence. Show more…
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In Exercises $91-98,$ assume that each sequence converges and find its limit. $$\sqrt{1}, \sqrt{1+\sqrt{1}}, \sqrt{1+\sqrt{1+\sqrt{1}}}$$ $$\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1}}}}$$
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