Learning Mathematica Basics—Arithmetic

Solve each of the following problems using Mathematica exclusively.

These problems should be completed using only the operators +, -, *, /, ^, !, %, the command N and the constants Pi, and E.

1.	Evaluate the sum of the even numbers from 2 to 10, inclusive.

2.	Raise 3 to the 50th power.

3.	Raise 2 to the 20th power, and divide this result by 20 factorial.  (Note: Mathematica automatically reduces the resulting fraction.  Also, ask yourself which operation, the taking of the power or the taking of the factorial, has the greater effect, i.e. the greater contribution to the answer.)

4.	Find the product of the odd numbers from 3 to 11, inclusive, and subtract 5 factorial from this result.

5.	Find the 5th root of 112, and express the answer to 20 significant digits.  (Note:  You may need to recall that roots can also be expressed as exponents.)

6.	Find the product of π and e to 50 significant digits.  (Note:  Remember to use the correct Mathematica syntax for these special constants.)

7.	Divide 126 by 36, leaving the answer as a reduced fraction.

8.	Express the previous result as a decimal with default precision. (Use the % shortcut.)

9.  Using a single command line:  Find the sum of the first 5 powers of e, (e through e5), then raise this result the power of the square root of π;  display your result as a decimal with 50 significant digits.

10.  Despite the fact that this is considered a bad practice in general, (just to show that you know how to do it), add together the results of problems 2, 6, and 7 using the % operator, and display your answer as a decimal with  10 significant digits.