Advanced Search

Question: What is the asymptotic value of the root?

Question:What is the asymptotic value of the root?

Rouben Rostamian 8003 Maple
roots asymptotic
June 16 2019
2

I am interested in the root of the equation ((2*n-1)*x + 2*n + 1)*x^n = 1 - x, where 0 < x < 1 and n is a large positive integer.  I believe that the root converges to 1 as n goes to infinity.  How does one obtain an asymptotic estimate of the root for large n?

 
Please Wait...