八度音阶的无穷级数之和

Question

Just started acquaintance with Octave. Trying to calculate the sum of an infinite series. Math is bad, can anyone help? In the code for x I took one. row formula

sum((-1)^([1:inf]+2)/factorial([1:inf])*1^[1:inf]);

Answer 1

Mathematically, the formula is

exp(-1/x)-1

which can derived from Taylor expansion.

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Symbolic verification

pkg load symbolic
syms x n
simplify(symsum((-1/x).^n./(factorial(n)),n,1,inf))

which gives

>> simplify(symsum((-1/x).^n./(factorial(n)),n,1,inf))
ans = (sym)

        -1
        ---
         x
  -1 + e

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Numeric verification

n = 20;
x = 2;

such that

>> sum((-1/x).^(1:n)./(factorial(1:n)))
ans = -0.39347
>> exp(-1/x)-1
ans = -0.39347