# arithmetic series expressed in sigma notation

• Feb 5th 2007, 01:38 PM
kcsteven
arithmetic series expressed in sigma notation
I know that an arithmetic series of n terms can be written :
a + (a+d) + (a+2d) +...+ [a+(n-1)d] but I am not sure how to write it in sigma notation, I was thinking the lower limit would start at 1 but what about the upper limit? And since the sum of the integers is increasing each time would it be (n+1)? Could a formula be written in terms of a, d and n for the sum of this series that would make sense to me? What I am trying to say is can you explain it so I can understand it. I would appreciat it, I hope this makes sense to you, I don't know if this sounds logical, I am just trying to understand sums of series.
Thank you!!!!!!!!!!
Keith Stevens
• Feb 5th 2007, 02:11 PM
Plato
$\displaystyle \sum\limits_{k = 0}^{n - 1} {\left( {a + kd} \right)} = \sum\limits_{k = 1}^n {\left( {a + \left( {k - 1} \right)d} \right)}$
• Feb 5th 2007, 02:56 PM
kcsteven
an arithmetic series of n terms
:) Thank you, I guess the light goes on a little slower for some than others, I am workin on speeding up the brain but sometime when I look at a problem or a question for a long period of time and do not understand, it is nice to have this forum to help make sense of it all.