Dataadapter.update() doesn't save anything

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C#

ADO.NET

DataTable

DataAdapter

Hi, i have a disconnected ado.net code. I am deleting some rows from a datatable. And then acceptchanges over datatable and then update for physically saving over dataadapter. If i don't put following line everything works fine otherwise there is no actual change on database: ds.Tables[0].AcceptChanges();
I wonder why accepting changes and then updating doesnt work.

SqlConnection conn = new SqlConnection(connectionString);
            conn.Open();
            SqlDataAdapter adapter = new SqlDataAdapter("select * from People", conn);
            SqlCommandBuilder cb = new SqlCommandBuilder(adapter);
            DataSet ds = new DataSet();

            adapter.Fill(ds);

            DataRow[] rows_filtered = ds.Tables[0].Select("cityID=1");
            foreach (DataRow item in rows_filtered)
            {
                item.Delete();
            }

            dataGridView1.DataSource = ds.Tables[0];
            //ds.Tables[0].AcceptChanges(); ***why this line causes trouble***
           adapter.Update(ds.Tables[0]);

What I have tried:

Not much yet. I am really confused about adapter.Update and datatable.AcceptChanges(). They seeem to be similar.