Random variables $X_1, X_2,...,X_n,..$ are independent and have uniform distributions on $(0,1)$. Random variable $N$ has Poisson distribution with expected value $2$ and they are independent from $X_1,X_2,...,X_n,...$. Calculate $Cov\left(\frac{X_1}{\sum_{i=1}^{N+1} X_i },N\right)$.
I started from calculation of $E\left(\frac{X_1}{\sum_{i=1}^{N+1} X_i }N\right)=\sum_{k=1}^{\infty} E\frac{X_1}{\sum_{i=1}^{k+1} X_i}\cdot k\cdot \mathbb{1}_{(N=k)}$. I have a problem how to calculate $E\frac{X_1}{\sum_{i=1}^{k+1} X_i}$. Thanks in advance for help.