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The autosum button will insert the function "=sum(...)" and suggest (highlight) a range it finds most likely - usually adjacent cells above, or to the left, of the cell where you insert the formula.
auto correlation function of a stationary process is an even function
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
That's called a built-in function; or often simply a "function".
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.