Page 83 - A Guide to MATLAB for Beginners and Experienced Users

64 Chapter 4: Beyond the Basics

Sums and Products
Finite numerical sums and products can be computed easily using the vector
capabilities of MATLAB and the commands sum and prod. For example,
>> X = 1:7;
>> sum(X)

ans =
28
>> prod(X)

ans =
5040

You can do finite and infinite symbolic sums using the command symsum.
To illustrate, here is the telescoping sum
n
1 1
− :
k 1 + k
k=1
>> syms k n; symsum(1/k - 1/(k + 1), 1, n)

ans =
-1/(n+1)+1
And here is the well-known infinite sum
∞
1
:
n 2
n=1
>> symsum(1/nˆ2, 1, Inf)

ans =
1/6*pi^2
Another familiar example is the sum of the infinite geometric series:

>> syms a k; symsum(aˆk, 0, Inf)

ans =
-1/(a-1)

Note, however, that the answer is only valid for |a| < 1.