 Quandaries and Queries Ken parent secodary a.) Explain the difference between the series from i=1 to n :ai and the series j=1 to n :aj b.) Explain the difference between the series from i=1 to n:ai and the series from i=1 to n :aj 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 Go to Math Central