- #1
iamhumble
- 28
- 0
Homework Statement
What is the sum of all the even numbers from 0 to 2n, for any positive integer n?
Homework Equations
does not apply
The Attempt at a Solution
On any other day I would be able to solve the problem within seconds. However, my brain is fried beyond repair at the moment.
First, I want to know if I understand the question correctly. So, I have the equation "0 to 2n" and when "n = 2" the equation will now be "0 to 4". Now, when I sum up all the even integers do I also include 4 or not? The word "to" is messing it up. I know it is lame but I can't think straight now.
I believe that I do include the even values from 0 to 4 when "n=2". If this is the case, the sum will be 2 + 4 = 6.
Here are other sum values I have computated:
when n = 3, sum is 2 + 4 + 6 = 12
when n = 4, sum is 2 + 4 + 6 + 8 = 20
when n = 5, sum is 2 + 4 + 6 + 8 + 10 = 30
when n = 4, sum is 2 + 4 + 6 + 8 = 20
when n = 5, sum is 2 + 4 + 6 + 8 + 10 = 30
I have be doing my best to develop an equation to satisfy the sum for any positive inter n and the only thing I could come up with is this.
given a positive n integer, take (n^n) + n to get the sum of all the even positive integer value
Wait. I just figured out the equation!
All I am asking assistance for is if I have the correct understanding above. Any suggestions will be nice.