1. Given an integer N, it is required to compute the sum of the cubes of the num

Question

1. Given an integer N, it is required to compute the sum of the cubes of the numbers from 1 to N. The sum can be computed directly or analytically by the following formula: S = 13 + 23 + 33 + · · · + N 3 = 1 4 N 2 (N + 1)2 (1) a. Let N = 20. Compute the sum by the following 5 methods, using: (1) a for-loop, (2) a conventional while-loop, (3) a forever while-loop, (4) the vectorized sum function, and, (5) the above analytical formula. b. Write a function, say, fsum.m, that employs a switch structure and evaluates the sum by any of the above 5 methods, with method 5 being the default method. It must have the following usage, where m is the method number, m = 1, 2, 3, 4, 5: S = fsum(N,m); c. The sum S grows with increasing N. Using your function fsum and a forever-while loop determine the smallest N such that S > 106 . Repeat using a conventional while-loop.

Explanation / Answer

i=1; sum=0; while (i < 10) cube = i * i * I; sum = sum + cube; i++; end while(true) cube = i * i * I; sum = sum + cube; i++; end for a = 10:20 sum += (a*a*a); end n=15; sum = pow(((n * (n + 1) ) / 2),2); for n = 1:15 V(n) = pow(((n * (n + 1) ) / 2),2); end

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