Home » Posts tagged 'Ramanujan'

Tag Archives: Ramanujan

On Ramanujan’s Nested Radicals

Friday, December 30th, 2011 08:50 / 8 Comments

Ramanujan (1887-1920) discovered some formulas on algebraic nested radicals. This article is based on one of those formulas. The main aim of this article is to discuss and derive them intuitively. Nested radicals have many applications in Number Theory as well as in Numerical Methods.
ramanujan

Solving Ramanujan’s Puzzling Problem

Thursday, February 3rd, 2011 14:07 / 11 Comments

Consider a sequence of functions as follows:-

f_1 (x) = \sqrt {1+\sqrt {x} }
f_2 (x) = \sqrt{1+ \sqrt {1+2\sqrt {x} } }

f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }

……and so on to

f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n \sqrt {x} } } } } }

Evaluate this function as n tends to infinity.

Or logically:

Find

\displaystyle{\lim_{n \to \infty}} f_n (x) .

(more…)

Follow

Get every new post delivered to your Inbox.

Join 755 other followers

%d bloggers like this: