Can I find the general term of this sequence an=√2+an−1, 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