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maramfaith24 · Jan 3, 2011, 12:51 PM

I've been working on an assignment for a few weeks now, I am way behind.. Can you offer help to the question?

jcaron2 · Jan 3, 2011, 08:52 PM

In sigma notation (also called summation notation) the letters k or n are often used to designate the index (though really any variable could be used). The index is incremented from the number in the subscript of the Sigma to the number in the superscript, the argument of the sigma is evaluated at each of those index values (the argument is usually some function of the index, k or n), and the resulting values (one for each index) are added together.

For example, if you wanted to add together all the numbers from 101 to 200, you could write

$\sum_{k=101}^{200} k$

Or if you wanted to add together all the fractions 1/2 + 1/3 + 1/4 + 1/5 +... forever, you could write

$\sum_{k=2}^{\infty} \frac{1}{k}$

So to reiterate, you can see from the above examples that the value to the right of "k=" is just the starting value for the index, while the value at the top of the sigma is the ending value. The argument (to the right of the sigma) is evaluated at all integer values from the starting value up to and including the ending value. The values of the argument at every one of those index values are then added together.