Chapter P, Problem 24PS

In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories:

Yes. I know how to start this problem.

No. I don’t think I know how to start this problem.

Hopeful. If someone shows me how to proceed, I think I could answer this question.

Hopeless. I don’t think I’ll ever be able to answer this question.

If $1+2+3+\dots +n=\frac{n(n+1)}{2}$, what is the sum of the first $\mathrm{100,\; 000}$ counting numbers beginning with $1$?