Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said, “Whoever fasts the month of Ramadan out of faith and seeking reward, then Allah will forgive all of his previous sins. Whoever stands in prayer during the Night of Decree out of faith and seeking reward, then Allah will forgive all of his previous sins.”

Source: Sahih Muslim 760

Grade: Sahih (authentic) according to Muslim

عن أبي هريرة أَنَّ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ مَنْ صَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ وَمَنْ قَامَ لَيْلَةَ الْقَدْرِ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ

760 صحيح مسلم كتاب صلاة المسافرين وقصرها باب الترغيب في قيام رمضان وهو التراويح

http://dailyhadith.abuaminaelias.com/2012/07/18/hadith-on-ramadan-the-virtue-of-fasting-during-ramadan-and-praying-during-the-night-of-decree/