IIT JEE , AIEEE Forum - Mathematics , Algebra

LAMPARD

,In maths, the Viète formula, named after Francois Viete, is the following infinite product type representation of the mathematical constant

1)divide the eqn by 2 and then take its reciprocal...
This resultant exp. matches wid exp. of Viete's formula..

The expression on the right hand side has to be understood as a limit expression

$\lim_{n \rightarrow \infty} \prod_{i=1}^n {a_i \over 2}=\frac2\pi$

where $a_n=\sqrt{2+a_{n-1}}$ with initial condition $a_1=\sqrt{2}.$

$\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots\!$
and so on till ...