Let {an} be a sequence of positive real numbers such that |an+2- an+1| < |an+1 -an|...

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Let {an} be a sequence of positive real numbers such that |an+2- an+1| < |an+1 -an| for all n belongs to N. Can we conclude from the above condition that the sequence {an} converges? Let {an} be a sequence of positive real numbers such that |an+2- an+1| < |an+1 -an| for all n belongs to N. Can we conclude from the above condition that the sequence {an} converges?

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