Further Maths - Sums of Cubes
Pearson Edexcel Further Mathematics 2022
The sum of cubes formula
What is the formula for the sum of the cubes of the first $n$ natural numbers?
\[\sum^{n} _ {r=1} r^3 = \frac{1}{4}n^2(n+1)^2\]
How could you rewrite $\sum^{n} _ {r=1} r^3$?
\[\frac{1}{4}n^2(n+1)^2\]
What’s another way of expressing $\frac{1}{4}n^2(n+1)^2$?
\[\sum^{n} _ {r=1} r^3\]
Remembering the formula
What’s an easy way for remembering the sum of cubes formula?
It’s the sum of the natural numbers formula squared.