A school’s annual day programme requires arranging chairs in rows such that the first row has 1 chair, the second row 2 chairs, the third row 3 chairs, and so on up to 100 rows.
(i) Calculate the total number of chairs required.
(ii) The event manager wants to know the sum of the squares of the row numbers, ∑k=1100k2, to decide on decorative ribbons for each chair. Find this sum.
(iii) Determine the sum of the cubes of the row numbers, ∑k=1100k3, and hence obtain the ratio ∑k=1100k2∑k=1100k3.