Hi Ken,

Suppose that you have the series

a1 + a2 + a3 + a4 + a5

The terms in the series are of the form

"a followed by an integer" where the integer varies between 1 and 5.

A neater way to write this series is to use a variable to represent the integer and say that the integer varies between 1 and 5. Suppose that I use the letter i represent the integers then the terms are of the form ai where i is 1, 2, 3, 4, or 5. Thus

"the series from i=1 to 5 :ai" is a1 + a2 + a3 + a4 + a5.

The letter that you use to represent the integer is unimportant. I could have used j rather than i and then

"the series from j=1 to 5 :aj" is a1 + a2 + a3 + a4 + a5.

If, however, you have the series

a2 + a2 + a2 + a2 + a2

and you want to write this in the same neat way then it would be

"the series from i=1 to 5 :a2" is a2 + a2 + a2 + a2 + a2.

or, as in your last example

"the series from i=1 to n :aj" is aj + aj + aj + ... + aj.

I used the ... notation since I don't know what n is. In fact in this last case you can write the series even more efficiently

"the series from i=1 to n :aj" is aj + aj + aj + ... + aj = n aj

Penny

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