Solve $x\sqrt{x\sqrt{x\sqrt{x\dots}}} = 4$ Today I faced a strange equation and I didn't manage to find a solution to it:
$$x\sqrt{x\sqrt{x\sqrt{x\dots}}} = 4$$
Maybe someone will help me to find a way to solve it. By the way, this equation is from high school course.
$$x\sqrt{x\sqrt{x\sqrt{x\cdots}}}=x\,x^{1/2}\,x^{1/4}\,x^{1/8}\cdots=x^{1+1/2+1/4+1/8+\cdots}=x^2$$
The power of given variabe is in the term of sum of G.P . The indices of x is such that 1+1/2+1/4+......
Because we know that the infinite sum of G.P:
Sn = a/(1-r) where r=common ratio