this post was submitted on 01 Jun 2026
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I had a student tasked with summing a finite geometric sequence with |r|>1, let's say 1+2+4+8+16. He had apparently forgotten the formula for that, but knew the formula for the infinite series a/(1-r). Good enough he thinks, and sums 1+2+4+... = -1, then subtracts off the excess terms 32+64+128+... = -32, and gets the correct answer of 31.
It is actually a completely correct calculation if you work in p-adic numbers or formal power series.
Indeed, and would have earned full marks had he said that, or even showed any awareness that his intermediate results were somehow nonstandard.