A modular structural analysis of a skyscraper uses a load-bearing index L(m)L(m)L(m) for the mmm-th floor. This index is calculated by the difference between two cumulative load sums:
L(m)=∑k=0m5k4−∑k=0m−15k4L(m) = \sum_{k=0}^{m} 5k^4 - \sum_{k=0}^{m-1} 5k^4L(m)=∑k=0m5k4−∑k=0m−15k4
where mmm is a positive integer representing the floor number.
Find the load-bearing index for the 4th floor, L(4)L(4)L(4), and the 10th floor, L(10)L(10)L(10).
An engineer determines that the maximum theoretical limit for a floor's load-bearing index is 3.125×10113.125 \times 10^{11}3.125×1011. Calculate the floor number mmm that reaches this limit.
Practise Edexcel A Level Maths 3.6 Sigma Notation with exam-style questions for A Level Maths. 7 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.