Abu Hurayrah (may Allah be pleased with him) reported: The Messenger of Allah (may Allah's peace and blessings be upon him) said: "Whoever fasts Ramadan, out of faith and in pursuit of reward, his past sins will be forgiven."
The Prophet (may Allah's peace and blessings be upon him) informs that if a person fasts the month of Ramadan out of faith in Allah and out of belief in the obligation of fasting and the abundant reward Allah Almighty has prepared for those who observe fast, seeking thereby Allah's pleasure, without show-off or pursuit of reputation among people, his past sins will be forgiven.