Magic Roots

Algebra Level 3

$\large \sqrt { 1+2\sqrt { 1+3\sqrt { 1+4\sqrt { 1+5\sqrt{\cdots} } } } } = \, ?$

2 solutions

Otto Bretscher
Feb 12, 2016

A celebrated result of Ramanujan... see the solution here

https://brilliant.org/problems/my-first-nested-radicals-problem/?group=2lCcdbx8bAkq&ref_id=1117451

similar problem

Hamza A - 5 years, 4 months ago

Abdelghani Ssoris
Feb 14, 2016

We note that:

We get

We substitute the value of (n+3) by putting l=3 in the first equation:

And so on:

Then we get the result, putting n=1:

Great,I never thought of that

Kaustubh Miglani - 5 years, 4 months ago