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- TL;DR Summary
- The physical meaning (if any) of this type of summation.

Hello, I was finding the average value of the expression ##(1-1/n^2)## for values from 1 to infinity by evaluating the limit as N→∞ for:

## \displaystyle\sum_{n=1}^{N} (1-1/n^{2})/N ##

and got what I expected, ##1##

What I didn't expect was to find that the general solution ##1-H_N^{(2)}/N## provided real values for ##N < 1##

Assuming that ##(1-1/n^2)## represents something physical, as in a statistical mechanics problem, what does it mean to summate from 1 upwards to something less than 1?

Thank you

## \displaystyle\sum_{n=1}^{N} (1-1/n^{2})/N ##

and got what I expected, ##1##

What I didn't expect was to find that the general solution ##1-H_N^{(2)}/N## provided real values for ##N < 1##

Assuming that ##(1-1/n^2)## represents something physical, as in a statistical mechanics problem, what does it mean to summate from 1 upwards to something less than 1?

Thank you

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