Of staircases and textbooks

October 27, 2009

This week, I’m talking you about a little identity that crops up often in the study of algorithms and which isn’t found in formula compendia—anyway, none that I have. I’m talking about this function:

\displaystyle C_{n,a}=\sum_{i=1}^n i a^i

This is a variation on the Gabriel’s Staircase function that does not have an infinite number of terms. Let us solve it without supposing that 0<a<1.

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