- #1
DivGradCurl
- 372
- 0
I used Mathematica to confirm that
[tex] \sum _{n=0} ^{\infty} \left[ \frac{\left( -1 \right) ^n \left( 2n \right) x^{2n+1}}{n! \left( n+1 \right) ! 2^{2n+1}} \right] + \sum _{n=0} ^{\infty} \left[ \frac{\left( -1 \right) ^n \left( 2n \right) \left( 2n+1 \right) x^{2n+1}}{n! \left( n+1 \right) ! 2^{2n+1}} \right] = - \sum _{n=0} ^{\infty} \frac{\left( -1 \right) ^n x^{2n+3}}{n! \left( n+1 \right) ! 2^{2n+1}} [/tex]
Does anyone know how to obtain it directly?
Thank you.
[tex] \sum _{n=0} ^{\infty} \left[ \frac{\left( -1 \right) ^n \left( 2n \right) x^{2n+1}}{n! \left( n+1 \right) ! 2^{2n+1}} \right] + \sum _{n=0} ^{\infty} \left[ \frac{\left( -1 \right) ^n \left( 2n \right) \left( 2n+1 \right) x^{2n+1}}{n! \left( n+1 \right) ! 2^{2n+1}} \right] = - \sum _{n=0} ^{\infty} \frac{\left( -1 \right) ^n x^{2n+3}}{n! \left( n+1 \right) ! 2^{2n+1}} [/tex]
Does anyone know how to obtain it directly?
Thank you.