Click: Start > All Programs > Mathematics > Mathematica.
Once Mathematica is open, click: File > Palettes > Basic Input.
In the Palette that opens (or may already have been open), click on the Sigma button (see below).
To move to the different "input boxes" of the Sigma, use Tab and Shift-Tab.
When done typing in the desired expressions, press Shift-Enter or the Enter key on your keyboard's number-pad.
For Problem 40, the answer will look like nonsense to you! Here's what's
happening:
Type in Sqrt[2] (or use the Basic Input palette) to find the square root of 2;
press Shift-Enter. What's the result? Mathematica doesn't give you
1.4142...; instead it gives you back what you typed in! Why? Because it
prefers to give you an exact answer. But you can tell it to give you
a decimal answer by typing in N[Sqrt[2]] ; try it! "N[ ]" means "give me a
Numerical answer".
Now go back to where you typed in your infinite series, and put N[ ] around it; then press Shift-Enter.
Mathematica gives you a complex number whose imaginary part is 0 times i , which is 0 (where i is the square root of -1). So the answer is just a real number.