The following example problem spells out in great detail how to translate a formula in summation notation into a Matlab
Recall this classic formula for due to Euler:
We can sum the first N terms of this series with the Matlab one-liner
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
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.