In 1887 an indian mathematician was born in Erode, a city in India (260km away from Madras). The indian mathematician's name was Srinivasa Ramanujan, who sent his letters to English mathematicians, in 1913 to publish his ideas. Ramanujan sent his letter, to one of the most famous mathematician in Britain at that time, Godfrey Harold Hardy. Hardy immediately recognized that Ramanujan is a genius. Hardy wanted Ramanujan, to come to Cambridge. 1914 April Ramanujan managed to arrive to England, where from that time on one of the most prosperous, and productive collaboration had begun between the two, in the history of mathematics, which lasted till the death of Ramanujan. The aim of my research is to give a simpler proof for one of Ramanujan's sum that was in his first letter.