Can I interchange the summation and integration of the following quantity ?
$$ \sum_{i=0}^{k-1} \binom{k-1}{i} (-1)^i \int_{T}^\infty e^{-(\frac{1}{\theta_1}-\frac{u}{k})(n-k+1+i)t}dt=\int_{T}^\infty\sum_{i=0}^{k-1} \binom{k-1}{i} (-1)^i e^{-(\frac{1}{\theta_1}-\frac{u}{k})(n-k+1+i)t}dt $$ Thanks in advance.