Sequence
Posted: Thu May 22, 2008 4:57 pm
\( x(0)>0 \)
\( x(n+1)=x(n) - e^{\frac{-1}{x(n)^2}} \)
Prove that \( x(n)=\frac{1}{\sqrt{\ln n}} - \frac{3}{4}\frac{\ln(\ln n)}{(\ln n)^{3/2}} + \frac{u(n)\ln(\ln n)}{(\ln n)^{3/2}} \)
with u(n) tend to 0 when n tend to infinity.
\( x(n+1)=x(n) - e^{\frac{-1}{x(n)^2}} \)
Prove that \( x(n)=\frac{1}{\sqrt{\ln n}} - \frac{3}{4}\frac{\ln(\ln n)}{(\ln n)^{3/2}} + \frac{u(n)\ln(\ln n)}{(\ln n)^{3/2}} \)
with u(n) tend to 0 when n tend to infinity.