What is the value of [math] \displaystyle \sum_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n+1}}}{4{{n}^{2}}-1}} [/math] ?
What is the value of [math]\sum_{n = 1}^{\infty}(-1)^{n-1}\frac{3}{n^4}[/math]?