MATLAB: Beginner’s question – why doesn’t a variable overwrite when vectorizing a loop

Question

I am learning using the book "Matlab for Engineers and Scientists." Unfortunately this book does not provide answers to the exercises.

I've never been good at writing for loops, or really understanding how to index well, so I am running into problems.

Here's the one at hand. I need to convert a for loop into a vectorization. For simplicity I've written a short example:

s=0;
for n=1:10;
    s=s+n
end

This gives the answers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. When I try to vectorize it like this, s does not overwrite itself after each iteration, but stays at zero:

s=0;
n=1:10;
s=s+n

This gives s=1:10.

Now if s is a simple variable to explain I could just make it a vector as well, but when I don't know what its values will be I can't specify it beforehand. Any help would be appreciated. I know this is simple, but going through this book, the earlier examples aren't relevant to this type of problem.

EDIT: Here is the actual question:

====================

Work out by hand the output of the following script for n = 4:

n = input( ’Number of terms? ’ );

s = 0;

for k = 1:n

s = s + 1 / (k ˆ 2);

end;

disp(sqrt(6 * s))

If you run this script for larger and larger values of n, you will find that the output approaches a well-known limit. Can you figure out what it is? Now rewrite the script using vectors and array operations. ====================

The limit is pi. When I try to do this with vectors I am entering the following:

====================

s=0;

n=4; (just to start)

k=1:1:n;

s=s+1./k.^2;

a=[sqrt(6.*s)];

====================

Of course, this doesn't work. What am I not getting? (Other that you can't overwrite variables if you aren't doing a for loop…but the exercise asks specifically to do this not using a for loop)

Answer 1

cumsum(1:10)