عن أبي هريرة -رضي الله عنه- مرفوعاً: «من صَام رمضان إيِمَانًا واحْتِسَابًا، غُفِر له ما تَقدَّم من ذَنْبِه».
[صحيح.] - [متفق عليه.]
المزيــد ...

Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "He who observes fasting during the month of Ramadan faithfully and expecting its reward from Allah will have his past sins forgiven."
[Sahih/Authentic] - [Al-Bukhari and Muslim]

Explanation

Allah will forgive the previous sins of the one who fasts the month of Ramadan, out of firm belief in Allah’s promise and sincerely expecting its reward from Allah, the Almighty. This does not apply to the one who fasts for showing off (his good deeds) and win good opinion of people.

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1: It points out the merit and high status of Ramadan and that it is the month of fasting. Whoever fasts it will have his sins and misdeeds forgiven, even if they were as much as the foam of the sea.
2: It is permissible to say 'Ramadan' without the word 'month'.