Evaluation in Iteration Functions
The built-in Mathematica iteration functions such as Table and Sum evaluate their arguments in a slightly special way.
When evaluating an expression like Table[f, {i, imax}], the first step, as discussed in "Blocks and Local Values", is to make the value of i local. Next, the limit 
in the iterator specification is evaluated. The expression f is maintained in an unevaluated form, but is repeatedly evaluated as a succession of values are assigned to i. When this is finished, the global value of i is restored.
The function
RandomReal[] is evaluated four separate times here, so four different pseudorandom numbers are generated.
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This evaluates
RandomReal[] before feeding it to
Table. The result is a list of four identical numbers.
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In most cases, it is convenient for the function f in an expression like Table[f, {i, imax}] to be maintained in an unevaluated form until specific values have been assigned to 
. This is true in particular if a complete symbolic form for f valid for any i cannot be found.
This defines
to give the factorial when it has an integer argument, and to give
(standing for "Not a Number") otherwise.
In this form,
is not evaluated until an explicit integer value has been assigned to
.
| Out[4]= |  |
Using
Evaluate forces
to be evaluated with
left as a symbolic object.
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In cases where a complete symbolic form for f with arbitrary i in expressions such as Table[f, {i, imax}] can be found, it is often more efficient to compute this form first, and then feed it to Table. You can do this using Table[Evaluate[f], {i, imax}].
The
Sum in this case is evaluated separately for each value of
.
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It is however possible to get a symbolic formula for the sum, valid for any value of
.
| Out[7]= |  |
By inserting
Evaluate, you tell
Mathematica first to evaluate the sum symbolically, then to iterate over
.
| Out[8]= |  |
| Table[f,{i,imax}] | keep f unevaluated until specific values are assigned to i |
| Table[Evaluate[f],{i,imax}] | evaluate f first with i left symbolic |
Evaluation in iteration functions.
