How can I solve this equation analytically. $$\sqrt{x+\sqrt{2x+\sqrt{3x...}}}-100x\sin(x)=0$$
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7Isn't zero a solution? – Nathaniel Bubis Nov 10 '14 at 18:31
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I want the roots of equation. – E.H.E Nov 10 '14 at 18:33
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3Is there any reason to believe a nonzero root can be obtained analytically? What is the source of this question? – Alex Wertheim Nov 10 '14 at 18:35
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I'm sure I'm missing something here, but for what values of $x$ is that root expression well-defined, i.e. converges? – Simon S Nov 10 '14 at 18:44
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@SimonS - for all $x>0$. – Nathaniel Bubis Nov 10 '14 at 18:46
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I see no reason for there to be an analytical expression. However, note that the root term increases like $\sqrt{x}$, so that as $x$ becomes large, the roots become closer and closer to $n\pi$.
Attached is a plot of the distance between the first hundred roots and $n\pi$. As you may see, the graph decreases logarithmically:
Nathaniel Bubis
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