Summation series using matlab

Question

When i write this in matlab

syms x;
f=x^3-cos(x);
g=diff(f)

it gives out put as

g =

3*x^2+sin(x)

Now I want to generate summation series as

I google and found "symsum" command but it doesn't do my required task, when i write the following commands

syms k
symsum(k^2, 0, 10)
symsum(1/k^2,1,Inf)

it gives the out put as

ans = 385

ans = pi^2/6

Can you guys guide me how can I genereate the series which produce output as

so that when I give command diff(Sk); it should produce result as or something like that

For example in Mathematica I can do it as

Your assistance will be surely of great help.

Answer 1

I have looked the help of the symsum function and you have a really good example, try this:

syms x;
syms k real;
symsum(x^k/sym('k!'), k, 0, inf)

This commands evaluate the series , and actually evaluates to . As you can see you have to specify the term of the series with its dependence of 'k'. Then in the symsum command you have to specify that you want to sum over 'k' from 0 to inf.

So for example, you could do the following:

syms x;
syms k real;
ak = (-1)^k*x^(2*k+1)/sym('(2*k+1)!');
sum_ak = symsum(ak, k, 0, inf);     % gives back sin(x)
dak = diff(ak,x);
sum_dak = symsum(dak, k, 0, inf);   % should give back cos(x), but does not
A5 = symsum(ak, k, 0, 5);           % add only the first values of the series
DA5 = symsum(dak, k, 0, 5);         % add the derivated terms of the series

You can declare multiple symbolic variables uk and add them up:

syms x;
syms k real;
n = 5;
for i = 0:n
    eval(['syms u',num2str(i),' real;']);
end

A = cell(1,n);
for i=1:n
    A{i} = u0;
    for j=1:i
        eval(['A{i} = A{i} + u',num2str(j),';']);
    end
end
A{3} % check the value of A{i}

Hope this helps,