computed columns, index, clustered index and covering index?
Computed Columns can be stored in the data page in one of two ways. Either by creating them as PERSISTED or by including them in the clustered index definition. 

If they are included in the clustered index definition then even if the columns are not marked as PERSISTED then the values will still be stored in each row. These index key values will additionally be stored in the upper level pages.

If the computed column is imprecise (e.g. float) or not verifiable as deterministic (e.g. CLR functions) then it is a requirement for the column to be marked as PERSISTED in order to be made part of an index key.

So to give an example

CREATE TABLE T
(
A INT,
C1 AS REPLICATE(CHAR(A),100) PERSISTED,
C2 AS REPLICATE(CHAR(A),200),
C3 AS CAST(A AS FLOAT) PERSISTED,
C4 AS CAST(A + 1 AS FLOAT)
)

CREATE UNIQUE CLUSTERED INDEX IX ON T(C2,C3)



C1 will be stored in just the data page rows as it is marked as
PERSISTED but not indexed. 
C2 will be stored in both the rows on the data page and the index higher levels as it is an index key column.
C3 will be stored as for C2. As it is imprecise it is a requirement to mark it as PERSISTED however.
C4 won't be stored anywhere as it is neither marked as PERSISTED nor indexed.


Similarly all computed columns referenced in non clustered index definitions as key columns need to be stored at all levels of the index as they are part of the index key. There is the same requirement regarding precise/deterministic results.

Fails

CREATE NONCLUSTERED INDEX IX2 ON T(A,C4)


With the error.  


  Cannot create index or statistics 'IX2' on table 'T' because the
  computed column 'C4' is imprecise and not persisted. Consider removing
  column from index or statistics key or marking computed column
  persisted.


To include it as part of the non clustered index key it must also be stored in the clustered index data pages. However

Succeeds.

CREATE NONCLUSTERED INDEX IX2 ON T(A) INCLUDE (C4)


Computed columns that are only INCLUDEd columns are persisted to the NCI leaf page and do not have the requirement that they also be persisted in the data page.