Graphics Programs Reference
In-Depth Information
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
k
−
:
1
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.
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