Sum 1 to N writes the following:
A math professor is proving some general theorem, and ends up with a result involving [tex]x[/tex]â€™s and [tex]y[/tex]â€™s. One student raises his hand and asks, â€œCan you show us a special case of that theorem?â€. In other words, the student wanted a specific application of the theorem. The professor proceeds to erase the [tex]x[/tex]â€™s and [tex]y[/tex]â€™s and replace them with [tex]x_0[/tex]â€™s and [tex]y_0[/tex]â€™s. The student replies, â€œAh! That makes more sense.â€
As it is trivially obvious to the most casual observer, the extension of the theorem to [tex]x_1[/tex] and [tex]y_1[/tex] is left as an exercise to the interested reader.
And it will be on the test.