It seems rational but is truly irrational

One definition of $\pi$ is: $\frac { 1 }{ \pi } =\frac { 2\sqrt { 2 } }{ 9801 } \sum _{ n=0 }^{ \infty }{ \frac { (4n)!(1103+26390n) }{ { (n!) }^{ 4 }{ 396 }^{ 4n } } }$ So with some simple algebra, we can get: $\sum _{ n=0 }^{ \infty }{ \frac { (4n)!(1103+26390n) }{ { (n!) }^{ 4 }{ 396 }^{ 4n } } } =\frac { 9801 }{ \pi \times 2\sqrt { 2 } }$ which makes the answer $1103+9801+2+2=\boxed{10908}$