What were the 13th, 14th and 15th amendments supposed to do and did they succeed?

The 13th Amendment abolished slavery

The 14th Amendment states all people born or naturalized in the United States are citizens

The 15th Amendment gives everybody the right to vote no matter that citizen's race or color

All of these succeed because they allowed all African Americans to be free from slavery and granted them the right to citizenship. All Amendments are still enforced to this day and will never be removed from the Constitution.