Monday, 2 November 2015

convergence divergence - Prove that the sequence: a1=1,an+1=sqrtc+dan (when the real numbers c,d>1) is converging and find it's limit

I have a summarized solution but it's starts with proving that the sequence is bounded from above by c+d.
How can I know that this sequence is bounded by c+d? I understand the proof by induction but how do I actually realize that fact?




I know how to prove that the sequence is monotonically increasing and to find it's limit after we've established that the sequence is converging.

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real analysis - How to find limhrightarrow0fracsin(ha)h

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