Homework Help: Find the terms that add up to 1010100

1. Feb 8, 2012

kscplay

1. The problem statement, all variables and given/known data
Which terms of this sequence add up to 1010100? (Don't need to be consecutive terms)

{an}n=1 = {n(n+1)/2}n=1
2. Relevant equations

3. The attempt at a solution
The sequence is made up of the sums of all the numbers less than and including n. Don't really know much more than that.

2. Feb 8, 2012

Joffan

Can you post $a_1, a_2, a_3, a_4, ..., a_{10}$? Just to show you're taking this problem seriously...

Now, for large n, $a_n\approx n^2/2$. Can you find the largest $a_n$ less than the target value?

3. Feb 8, 2012

kscplay

I just recopied the problem exactly as it was stated. But anyways I've already found the solution. Thanks :)

4. Feb 10, 2012

Joffan

No problem. There is actually one solution that involves adding just two triangular numbers together, $a_p+a_q=1010100$.

... $a_{899}+a_{1100}=1010100$ ...

Just as a matter of interest, how did you solve it?

5. Apr 6, 2012

kscplay

You're solution is much shorter than mine. How did you do it? I don't know much about triangular numbers. I separated 1010100 in to = 10002 + 1002 + 102. I noticed the pattern that $n^2=a_{n}+a_{n-1}$

So then I proved that: $[\frac{n(n+1)}{2}]+[\frac{(n-1)n}{2}]=n^2$
Afterwards, it was easy: $$1000^2+100^2+10^2= (a_{1000}+a_{999}+a_{100}+a_{99}+a_{10}+a_{9})$$

btw sorry for the late response.

6. Apr 6, 2012

Joffan

That's a neat use of pattern, well done.

I used my standard "engineering" approach: Excel :-).