Natural sum

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
Age
14 to 16
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Natural Sum

The picture illustrates the sum $1 + 2 + 3 + 4 = (4 \times5)/2$. Prove the general formula for the sum of the first $n$ natural numbers and the formula for the sum of the cubes of the first n natural numbers. See the problem Picture Story .