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.