Repetitive Operations
In using
Mathematica, you sometimes need to repeat an operation many times. There are many ways to do this. Often the most natural is in fact to set up a structure such as a list with many elements, and then apply your operation to each of the elements.
Another approach is to use the
Mathematica function
Do, which works much like the iteration constructs in languages such as C and Fortran.
Do uses the same
Mathematica iterator notation as
Sum and
Product, described in
"Sums and Products".
| Do[expr,{i,imax}] | evaluate expr with  running from 1 to  |
| Do[expr,{i,imin,imax,di}] | evaluate expr with  running from  to  in steps of di |
| Print[expr] | print expr |
| Table[expr,{i,imax}] | make a list of the values of expr with  running from 1 to  |
Implementing repetitive operations.
This prints out the values of the first five factorials.
It is often more useful to have a list of results, which you can then manipulate further.
| Out[2]= |  |
If you do not give an iteration variable,
Mathematica simply repeats the operation you have specified, without changing anything.
| Out[3]= |  |
