Ramanujan style double nested expression

Algebra Level pending

Simplify the following expression:

\( \sqrt{5 + \sqrt{6 + 2\sqrt{7 + 3\sqrt{8 + 4\sqrt{9 + 5\sqrt{10 + 6\sqrt{11 + 7\sqrt{...}}}}}}}} \)

The pattern here is that the coefficients in front of the square root is the sequence 1,2,3..., Pattern(n) = n, starting at n = 1

The terms being added to the square roots are 5,6... Pattern(n) = 4 + n, starting at n = 1

================================================================

SPOILER ALERT

Solution technique can be found: http://vixra.org/pdf/1310.0177v1.pdf

×

Problem Loading...

Note Loading...

Set Loading...