X - sqrt-1 - sqrt-1 - sqrt-1 - sqrt-1 - - then-x - 10 2 but finite

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$x = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + . . . .}}}}$ , then:
$x = 1$
$0 < x < 1$
$1 < x < 2$
$x > 2$ but finite

0 < x < 1

x = 1

1 < x < 2

x > 2

but finite

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