Sr Examen
Otras calculadoras
- Serie de Taylor paso a paso
- Serie de Fourier paso a paso
- Ecuaciones diferenciales paso a paso
- Producto de la serie
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¿Cómo usar?
- Suma de la serie:
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(-1)^(n+1)/n
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2^n/n!
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(2*n-1)/2^n
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((-1)^(n+1))/n
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Expresiones idénticas
- nx^n/((8n- nueve)* tres ^n)
- nx en el grado n dividir por ((8n menos 9) multiplicar por 3 en el grado n)
- nx en el grado n dividir por ((8n menos nueve) multiplicar por tres en el grado n)
- nxn/((8n-9)*3n)
- nxn/8n-9*3n
- nx^n/((8n-9)3^n)
- nxn/((8n-9)3n)
- nxn/8n-93n
- nx^n/8n-93^n
- nx^n dividir por ((8n-9)*3^n)
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Expresiones semejantes
- nx^n/((8n+9)*3^n)
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Expresiones con funciones
- nx
- nx^n!
- nx^n/(n+2)
- nx^(n-2)
- nx^6n
- nx^n/3^n(n+1)
Suma de la serie nx^n/((8n-9)*3^n)
Solución
Ha introducido
[src]
oo ____ \ ` \ n \ n*x ) ------------ / n / (8*n - 9)*3 /___, n = 2
$$\sum_{n=2}^{\infty} \frac{n x^{n}}{3^{n} \left(8 n - 9\right)}$$
Sum((n*x^n)/(((8*n - 9)*3^n)), (n, 2, oo))
Respuesta
[src]
/ / / pi*I\ / 5*pi*I\ / 7*pi*I\ / pi*I\ / 3*pi*I\ / 3*pi*I\\ | | | ----| -3*pi*I | ------| -pi*I | ------| pi*I | ----| 3*pi*I | ------| | ------|| | | / 7/8 8 ___\ / 7/8 8 ___ pi*I\ | 7/8 8 ___ 2 | ------- | 7/8 8 ___ 4 | ------ | 7/8 8 ___ 4 | ---- | 7/8 8 ___ 4 | ------ | 7/8 8 ___ 4 | | 7/8 8 ___ 2 || | | 7/8 | 3 *\/ x | 7/8 | 3 *\/ x *e | 7/8 | 3 *\/ x *e | 7/8 4 | 3 *\/ x *e | 7/8 4 | 3 *\/ x *e | 7/8 4 | 3 *\/ x *e | 7/8 4 | 3 *\/ x *e | 7/8 | 3 *\/ x *e || | | 63*3 *log|1 - ----------| 63*3 *log|1 - ----------------| 63*I*3 *log|1 - ----------------| 63*3 *e *log|1 - ------------------| 63*3 *e *log|1 - ------------------| 63*3 *e *log|1 - ----------------| 63*3 *e *log|1 - ------------------| 63*I*3 *log|1 - ------------------|| | 2 | 7 \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 / \ 3 /| |2*x *|- ---------- - --------------------------- + --------------------------------- - ----------------------------------- - -------------------------------------------- - ------------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------| | | 16*x 7/8 7/8 7/8 7/8 7/8 7/8 7/8 7/8 | | | -16 + ---- 128*x 128*x 128*x 128*x 128*x 128*x 128*x 128*x | | \ 3 / |x| |-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- for --- < 1 < 63 3 | | oo | ____ | \ ` | \ -n n | \ n*3 *x | / -------- otherwise | / -9 + 8*n | /___, | n = 2 \
$$\begin{cases} \frac{2 x^{2} \left(- \frac{7}{\frac{16 x}{3} - 16} - \frac{63 \cdot 3^{\frac{7}{8}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} - \frac{63 \cdot 3^{\frac{7}{8}} e^{\frac{i \pi}{4}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{i \pi}{4}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} - \frac{63 \cdot 3^{\frac{7}{8}} i \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{i \pi}{2}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} - \frac{63 \cdot 3^{\frac{7}{8}} e^{\frac{3 i \pi}{4}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{3 i \pi}{4}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} + \frac{63 \cdot 3^{\frac{7}{8}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{i \pi}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} - \frac{63 \cdot 3^{\frac{7}{8}} e^{- \frac{3 i \pi}{4}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{5 i \pi}{4}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} + \frac{63 \cdot 3^{\frac{7}{8}} i \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{3 i \pi}{2}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}} - \frac{63 \cdot 3^{\frac{7}{8}} e^{- \frac{i \pi}{4}} \log{\left(- \frac{3^{\frac{7}{8}} \sqrt[8]{x} e^{\frac{7 i \pi}{4}}}{3} + 1 \right)}}{128 x^{\frac{7}{8}}}\right)}{63} & \text{for}\: \frac{\left|{x}\right|}{3} < 1 \\\sum_{n=2}^{\infty} \frac{3^{- n} n x^{n}}{8 n - 9} & \text{otherwise} \end{cases}$$
Piecewise((2*x^2*(-7/(-16 + 16*x/3) - 63*3^(7/8)*log(1 - 3^(7/8)*x^(1/8)/3)/(128*x^(7/8)) + 63*3^(7/8)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(pi*i)/3)/(128*x^(7/8)) - 63*i*3^(7/8)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(pi*i/2)/3)/(128*x^(7/8)) - 63*3^(7/8)*exp(-3*pi*i/4)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(5*pi*i/4)/3)/(128*x^(7/8)) - 63*3^(7/8)*exp(-pi*i/4)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(7*pi*i/4)/3)/(128*x^(7/8)) - 63*3^(7/8)*exp(pi*i/4)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(pi*i/4)/3)/(128*x^(7/8)) - 63*3^(7/8)*exp(3*pi*i/4)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(3*pi*i/4)/3)/(128*x^(7/8)) + 63*i*3^(7/8)*log(1 - 3^(7/8)*x^(1/8)*exp_polar(3*pi*i/2)/3)/(128*x^(7/8)))/63, |x|/3 < 1), (Sum(n*3^(-n)*x^n/(-9 + 8*n), (n, 2, oo)), True))
Ejemplos de hallazgo de la suma de la serie
- Suma de la serie de potencias
x^n/n
(x-1)^n
- Factorial
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
- Serie de Flint Hills
csc(n)^2/n^3
- Serie de cuadrados inversos
1/n^2
1/n^4
1/n^6
- Serie armónica
1/n
- Serie de Grandi
(-1)^n
- Serie alternada
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
- Serie de Newton-Mercator
(-1)^(n + 1)/n*x^n
- Investigar la convergencia de la serie
(3*n - 1)/(-5)^n