Infinite Fractions - 9

Algebra Level 2

$\sqrt { \frac { 1 }{ 2016 } +\sqrt { \frac { 1 }{ 2016 } +\sqrt { \frac { 1 }{ 2016 } +\cdots } } } =?$

Note : Round answer to the nearest whole number.

1 solution

Aditya Narayan Sharma
Mar 9, 2016

$\sqrt { \frac { 1 }{ 2016 } +\sqrt { \frac { 1 }{ 2016 } +\sqrt { \frac { 1 }{ 2016 } +\cdots } } } =?$

Denote It by X.

$X = \sqrt{X + \frac{1}{2016}}$

$X^2 = X + \frac{1}{2016}$

We get a quadratic in X , and solving we get X = 1.000 (approx) .