This is a story that seems to be an obligatory mention in either sequence and series lessons or exponential functions and today I've decided to track down the transmission of this story. it goes like this:
One of the most famous legends about series concerns the long inventor of chess whose name is lost the ages. According to the legend, an Indian king summoned the inventor and suggested that he chose the award for the creation of the interesting and wise game. The king was amazed by the “modest” request from the inventor who asked to give him for the first cell of the chessboard 1 grain of wheat, for the second—2 grains, for the third—4 grains, for the fourth—twice as much as in the previous cell, etc. As a result, the total number of grains per 64 cells of the chessboard would be number 18,446,744,073,709,551,615 (18 quintillion, 446 quadrillion, 744 trillion, 73 billion, 709 million, and 551,615). If the king was able to have that much of wheat, he would have to plant it everywhere on the entire surface of the Earth including the territories of the seas and oceans, and mountains, and the desert, from the Arctic to the Antarctic in order obtain a satisfactory harvest, then, perhaps, he maybe could pay his amazing debt off to the chess inventor in over 5 years.
[ Methods of Solving Sequence and Series Problems - Ellina Grigorieva pg191 ]
This is not exactly a hard hitting question but it would be nice to know at least the earliest mention of the story.