Stage 4 · Change and Relations / #29
Summing an Arithmetic Series: Flip It and Add
Planned
The video is in production. Follow along on GitHub to hear when it is out.
The idea
Draw the sum as a staircase of dots, copy it, turn the copy half a turn and fit it on: you get a rectangle. Every row is first term plus last term, there are as many rows as terms, so the sum is the number of terms times first plus last, divided by two.
A common mix-up
Pairing first with last only works for sums that start at one, like one up to a hundred.
Where it stops working
In one plus two plus four plus eight the steps aren't equal: flip and fit, and some rows have nine dots while others have six. No rectangle.
School year
China 高一/高二