Evaluation in Iteration Functions

The builtin Wolfram Language 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 imax 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 Null. This is true in particular if a complete symbolic form for f valid for any i cannot be found.

This defines fac to give the factorial when it has an integer argument, and to give NaN (standing for "Not a Number") otherwise:
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In this form, fac[i] is not evaluated until an explicit integer value has been assigned to i:
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Using Evaluate forces fac[i] to be evaluated with i 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 i:
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It is however possible to get a symbolic formula for the sum, valid for any value of i:
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By inserting Evaluate, you tell the Wolfram Language first to evaluate the sum symbolically, then to iterate over i:
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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.