SEAMO X 2020 — Paper E — Grade 9–10 Question 9

For $\lfloor x\rfloor$ denoting the greatest integer not exceeding $x$, evaluate $S=\left\lfloor\frac{2^2}3\right\rfloor+\left\lfloor\frac{3^2}4\right\rfloor+\cdots+\left\lfloor\frac{99^2}{100}\right\rfloor$.