The Louvre pyramid in Paris, France, is built of glass panes. There are 4 panes in the top row, and each additional row has 4 more panes than the previous row. 1.Write a series in summation notation to describe the total number of glass panes in n rows of the pyramid. 2.If the pyramid were made of 18 complete rows, how many panes would it have? 3.The actual pyramid has 11 panes less than a complet 18-row pyramid because of the space for the entrance. Find the total number of panes in the Louvre pyramid.
So the first row has 4 panes, the second 8, the third 12, and so on. The nth row would have 4n panes. 1. The total number of glass panes in n rows is 4*1 + 4*2 + 4*3 + ... + 4n or, in summation notation: n ∑ 4i i=1 2. n=18 4*1 + 4*2 + 4*3 + ... + 4*18 = 4 (1+2+3+ ... + 18) = 4 * 18 * 19 / 2 [using the well-known formula for triangular numbers*] = 36*19 = 684 * T(n) = n(n+1)/2 3. 684-11 = 673
