write the series 6+12+18+24 with summation notation
The terms are the first four multiples of 6.
Each successive term is 6 times the next integer.
So we could write it:
The k=1 on the bottom indicates that we are to start out
by substituting k=1 into the formula "6k", so we start with:
6(1)
then we put a + sign after that,
6(1)+
Then we substitute k=2 into the formula "6k" getting 6(2) so
we annex that on and now we have:
6(1)+6(2)
then we put a + sign after that,
6(1)+6(2)+
Then we substitute k=3 into the formula "6k" getting 6(3) so
we annex that on and now we have:
6(1)+6(2)+6(3)
then we put a + sign after that,
Then we substitute k=4 into the formula "6k" getting 6(4) so
we annex that on and now we have:
6(1)+6(2)+6(3)+6(4)
and we stop there because the 4 on top of the summation tells
us to quit when we get to 4. And the above is equivalent to
6+12+18+24
We can choose other letters for the dummy variable.
Any of the following would be just as good an answer:
We can technically use any letter for the dummy variable,
but usually the dummy variable is chosen as a lower case
letter taken from the middle of the alphabet somewhere,
like i,j,k,m,m. The letter 'small l' isn't used much as a dummy
variable because it looks too much like the number 1.
Edwin
