To help sort this out, here's some more information:
Schalim Bergerson (my great-grandfather) was born September 15, 1867.When he came to the United States in 1902, he came to join his brother-in-law, Tralke (?) Goldberg.If this is right, then I guess Shalim had a sister already in New York.Schalim died August 12,1936 in New York.
Isaac Bergerson (Shalim's brother) was born January 10, 1881.He died October 20, 1925 in New York.
Also, in alot of the records (ship records, citizenship records, marriage records) the last name is shown as "Bergersohn".