Monday, 24 December 2012

calculus - Is there a general form for an=sqrt2+an1?




Can I find the general term of this sequence an=2+an1, a1=2? I have proved the convergence. And found its limit. But is there any general form for it?


Answer



Hint: If an=2cos(θn) with 0<θn<π/2, then:




2+an=2+2cos(θn)



=2(1+cos(θn))/2



=2cos((θn)/2) using the appropriate half-angle formula.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...