tmua.me Extreme Set A Paper 1 · Question 11

A real number $r$ satisfies $0<r<1$ . For each integer $n\ge0$ , the point $P_n$ has coordinates

P_n=(r^n,r^{2n}).

A broken line joins $P_0$ to $P_1$ , $P_1$ to $P_2$ , and so on. The total area between this broken line and the $x$ -axis for $0\le x\le1$ is $\dfrac7{18}$ .

What is the value of

\sum_{n=0}^{\infty}\bigl(r^n-r^{2n}\bigr)?

\dfrac27

\dfrac{2\sqrt{33}}{33}

\dfrac{\sqrt{33}-3}{6}

\dfrac{\sqrt{33}+3}{6}

\dfrac{\sqrt{33}}2

\dfrac72

examday

tmua.me Extreme Set A Paper 1 · Q11