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# Math 445 lecture 10: more ''for''

The following example problem spells out in great detail how to translate a formula in summation notation into a Matlab for loop.

Recall this classic formula for due to Euler:

We can sum the first N terms of this series with the Matlab one-liner

N=100; sum((1:N).^(-2))

We can also do the sum with a for loop. To see how to build the for loop, it's helpful to think of the series as a sequence of partial sums

etc. Note that the difference between successive partial sums is a single term.

So we can compute the th partial sum by successively adding the term for n going from 1 to N.

That's exactly we do when we compute the sum with a for loop.

N=100;
P=0;
for n=1:N
P = P + 1/n^2;
end

At each step in the for loop, we compute for the current value of , add it to the previously computed partial sum , and then store the result into . But, since we are only interested in the final value , we just store the current value of the partial sum in the variable P and write over it with the next value each time we step through the loop.