ellipse and annulus
1) An ellipse with semi axes a and b fits between two circles of radii a and b (where b > a) as shown in the diagram. If the area of the ellipse is equal to the area of the annulus what is the ratio b:a?

(2) Find the value of R if this sequence of 'nested square roots' continues indefinitely:
R=   æ
 ú
Ö

1 +   æ
Ö

1 +
Ö

1 + [(1 + ...)]
 
 
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