1, -1, 1, -1, 1, -1, ……..

The sum of terms oscillates between 1 and zero depending on whether you've reached an odd term or an even.

But then I thought: can you really refer to this as a limit if we're not getting closer and closer to a value?

Here's an example where the terms do tend to a limit but oscillating either side of that value:

1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, …….

The numbers are successive numbers in the Fibonacci sequence (term r+2 is calculated by adding term r and term r+1) and tends to the golden ratio, 1.618....

Bob

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