CS100M Section (Lab) Exercise 4
1for-loop review
For each of the following sub-problems, complete the program so that it produces the desired result.
Do this on paper first and then check your solution using Matlab. You should not modify the given
code in any way—only fill in the blanks that are provided. In every case you will need to use for-loops
with an “increment” that is not one.
1. The following program reads an integer k, and outputs all the multiples of kup to 1000.
k = input(’Please enter a positive integer smaller than 1000: ’);
for j = ______________________
disp(j)
end
2. The following program reads in a real number xand an integer N, and computes the sum
PN
k=0
(−1)kx2k
(2k)! to the first Nterms. (This sum converges to cos(x)asN→∞.)
x = input(’Please input a real number between 0 and pi/2: ’);
N = input(’Please input a positive integer: ’);
sum = 0;
for j = _______________________
sum = sum + (-1)^(j/2) * x^j / factorial(j);
end
disp(sprintf(’The sum of the first %d terms is %12.8f\n’, N, sum))
3. The following does the same thing as in part (2) above, but this time we are not allowed to use
exponentiation and the factorial function, and must compute these explicitly.
x = input(’Please input a real number between 0 and pi/2: ’);
N = input(’Please input a positive integer: ’);
sum = 1; % Explicitly assign the first term (when j=0)
sign = 1; % The sign of a term, either 1 or -1
jfact = 1; % Current value of j!
xtoj = 1; % Current value of x^j
for j = _________________________
sign = ________________________________;
jfact = ________________________________;
xtoj = ________________________________;
sum = ____________________________________________;
end
disp(sprintf(’The sum of the first %d terms is %12.8f\n’, N, sum))
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