Expert: Sherman D. - 2/3/2006

Question
Hello,

I'm working on a proof for mathematical induction that the sum of the first n numbers is equal to n(n+1)/2.  What is meant in this question by the “…sum of the first n numbers…”.  I'm interpretting it as (n^2 + n) = n(n+1)/2, but this only works for 0,1 and after that it's an inequality.  When I used incrementally 0,1,2,3,4,5, and 6 I obtained 0,1,3,6,10,15, and 21 respectively, but this doesn't seem to have show any special pattern to me.  I can definitely see how n(n+1)/2 is a constant, but I'm confused about what is meant by  “…sum of the first n numbers…” in this particular instance.  What's a simple example I could start with?

Eddie.  

Answer
i believe what you are wanting is

n
E k = (n(n + 1))/2
k = 1

http://mathforum.org/library/drmath/view/56985.html

whereas "n" stands for the nth set of numbers, "k = 1" is the pattern, and "k" is the equation

for ex:

n = 4
E k
k = 1

That means 4 numbers, equation k, and pattern is 1.

1 + 2 + 3 + 4 = (4(4 + 1))/2
10 = (4(5))/2
10 = 20/2
10 = 10

which as you can see works.

Is this what you were looking for.