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GAOKAO · Sequences & Series · Advanced

Sequences & Series: Nested math: positive value?

Arithmetic/geometric, summation.

Try the problem

Nested 6+6+⋯\sqrt{6+\sqrt{6+\cdots}}: positive value?

Hint and answer

Concept to use

Telescoping sums.

Hint

Solve x2=6+xx^2=6+x.

Answer

3

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