Tintin has crash-landed in the jungle.
There is a village somewhere nearby, direction unknown.
So Tintin comes up with a cunning plan:
Fill up a water bottle from the plane, and take a compass,
Then walk 1 km north, change direction and walk 2 km east, then 3 km south, 4 km west, 5 km north, 6 km east, and so on, like this:
This way he will find the village no matter what direction it is in, and can (hopefully) find his way back to the plane for fresh water and shade when he needs it.
But he needs to know, at the end of each stage:
How far he has walked altogether?
How far (in a straight line) back to the plane?
How to sum the integers from 1 to n?
Given two whole numbers m and n such as n<m,
compare m(1 + 2 + 3 + …+ n) and n(1 + 2 + 3 +…+ m).