Sum - Qurak function reference

Symbolic summation.

Verificable de forma independiente: una respuesta de esta función se vuelve a derivar por otra vía y se compara; el taller y la herramienta verify lo hacen automáticamente, así una respuesta errónea se detecta en lugar de confiar en ella. Historial →

Formas

Sum[f, {i, imax}]

Sum[f, {i, imin, imax}]

Sum[f, {i, imin, imax, di}]

Sum[f, {i, {i1, i2, …}}]

Sum[f, {i, imin, imax}, {j, jmin, jmax}, …]

Sum[f, i]

Ejemplos verificadosSum[k, {k, 1, 10}] → 55 Sum[k^2, {k, 1, n}] → (n*(1 + n)*(1 + 2*n))/6 Sum[1/k^2, {k, 1, Infinity}] → Pi^2/6 Sum[(-1)^n x^(2n+1)/Factorial[2n+1], {n, 0, Infinity}] → Sin[x]Sum[n, {n, 1, 10}, Method -> Automatic] → 55 Sum[n, {n, 1, Infinity}, Regularization -> "Dirichlet"] → -1/12 Sum[n^3, {n, 1, Infinity}, Regularization -> "Dirichlet"] → 1/120 Sum[(-1)^n, {n, 1, Infinity}, Regularization -> "Abel"] → -1/2 Sum[(-1)^n n, {n, 1, Infinity}, Regularization -> "Abel"] → -1/4 Sum[1/n, {n, 1, Infinity}, Regularization -> "Dirichlet"] → Sum[n^(-1), {n, 1, Infinity}, Regularization -> Dirichlet]Opciones

Assumptions — default $Assumptions
GenerateConditions — default False
GeneratedParameters — default None
Method — default Automatic
Regularization — default None
VerifyConvergence — default True

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Usada en

Create a wavelet matrix plot - 1 paso
Is this price fair: present value and the break-even rate - 5 pasos
Evaluate infinite sums and products - 7 pasos

Temas

Additive Number Theory - Summation-Related Operations
Analytic Number Theory - Operations
Calculus - Discrete Calculus »
Discrete Calculus - Sums & Differences
Discrete Mathematics - Discrete Calculus »
Integer Functions - Digit-Based Substitution System Functions

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Total Plus Product NSum AsymptoticSum SumConvergence GeneratingFunction ZTransform FourierSequenceTransform DiscreteConvolve RSolve Integrate