Respuestas - Sección 5.3

Aquí encontrarás respuestas de los ejercicios de la sección 5.3

  1. f(x)=12+1π∑n=1∞[1−(−1)n]nsen(nx)\hspace{0.5cm} f(x)=\dfrac{1}{2}+\dfrac{1}{\pi}\sum_{n=1}^{\infty}{\dfrac{\left[1-\left(-1\right)^n\right]}{n}sen(nx)}

  2. f(x)=12+3π∑n=1∞[1−(−1)n]nsen(nx)\hspace{0.5cm} f(x)=\dfrac{1}{2}+\dfrac{3}{\pi}\sum_{n=1}^{\infty}{\dfrac{\left[1-\left(-1\right)^n\right]}{n}sen(nx)}

  3. f(x)=34+∑n=1∞(−1)n−1n2π2cos(nπx)−1nπsen(nπx)\hspace{0.5cm} f(x)=\dfrac{3}{4}+\sum_{n=1}^{\infty}{\dfrac{\left(-1\right)^n-1}{n^2\pi^2}cos({n}\pi x)-\dfrac{1}{n\pi}sen(n\pi x)}

  4. f(x)=14+∑n=1∞(−1)n−1n2π2cos(nπx)+(−1)n+1nπsen(nπx)\hspace{0.5cm} f(x)=\dfrac{1}{4}+\sum_{n=1}^{\infty}{\dfrac{\left(-1\right)^n-1}{n^2\pi^2}cos({n}\pi x)+\dfrac{\left(-1\right)^{n+1}}{n\pi}sen(n\pi x)}

  5. f(x)=π+∑n=1∞2n(−1)n+1sen(nx)\hspace{0.5cm} f(x)=\pi+\sum_{n=1}^{\infty}{\dfrac{2}{n}\left(-1\right)^{n+1}sen(nx)}