A conjecture

2

I was too hasty to generalize an observation. Here's my conjecture (which was easily rejected by a counterexample by no less than James Yorke of University of Maryland):

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Let {c_n} be a convergent infinite sequence that does not converge to a constant sequence. Derive another infinite sequence {d_n} as follows:

d_n=(c_n-c_n-1)/(c_n+1-c_n)

Then, {d_n} is also convergent.

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Unable to prove or disprove the conjecture, I emailed several mathematicians around the world to contaminate the challenge. Within few hours, James Yorke replied. Days later, Richard Taylor of Harvard University provided another counterexample. Actually, I am not sure if Taylor's sequence was really a counterexample since I did not check it out. The third counterexample, similar to Yorke's, is from my masteral thesis adviser and theoretical physics buddy Perry Esguerra of University of the Philippines.

I thank them all.