Abu Hurairah (May Allah be pleased with him) reported: The Messenger of Allah [SAWW](PBUH) used to urge (the people) to perform (optional Tahajjud) prayer at night during the month of Ramadan. He did not order them or make it obligatory on them. He [SAWW](PBUH) said, "Whosoever performs (optional Tahajjud) prayers at night during the month of Ramadan, with Faith and in the hope of receiving Allah's reward, will have his past sins forgiven.''
[Muslim Book 04, Chapter 52, Hadith # 210].