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Connection strings for SQL Server 2008[
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Also one nice way to resolve server name and instance is to open Sql Server Management Studio, connect to the database and then in the properties box, you should see the server name and instance.
Addition:
Example of current connection string to a local Sql Server database:
Server=(local)\MyInstance;Database=TestDatabase;Trusted_Connection=True;
Example of a connection string that clients use to connect to a single Sql Server database:
Server=ServerXYZ\TheInstanceName;Database=ProductionDatabase;Trusted_Connection=True;