Asher Falcon TMUA Paper 1 · Question 10

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Asher Falcon TMUA Paper 1 · Q10

Paper 1CalculusGeometry

Let $f(n)$ be defined as the total area of all the equilateral triangles starting with side length $n$ and then being successively halved.

What is the value of

\int_0^2 f(n)\,\dd n?

\frac{2\sqrt3}9

\frac{5\sqrt3}9

\frac83

\frac89

\frac{24\sqrt3}7

\frac{8\sqrt3}9

\frac{8\sqrt3}3

\frac{5\sqrt3}3

\sqrt3

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