# How write a linear operator of a sum?

Suppose I have a linear operator $\mathcal{L}$ and $w(x)=c_1u_1(x)+c_2u_2(x)$, $c_{1,2}$ are constants, so $$\mathcal{L}[w(x)]=\mathcal{L}[c_1u_1(x)+c_2u_2(x)]=c_1\mathcal{L}[u_1(x)]+c_2\mathcal{L}[u_2(x)] \tag{1}$$ However, if $w(x)$ is a sum to $N$ (or maybe infinite), i.e. $w(x)=\sum_{i=1}^{N}c_iu_i(x)$, can I somehow write $$\mathcal{L}[w(x)]= \mathcal{L}\Big [\sum_{i=1}^{N}c_iu_i(x) \Big]= c_i\mathcal{L} \Big [\sum_{i=1}^{N}u_i(x)\Big] \quad \text{?}$$ I guess $\sum_{i=1}^{N}c_iu_i(x) = \sum_{i=1}^Nc_i \sum_{i=1}^{N}u_i(x)$ is wrong?

I want to move the constants $c_i, i=1,2, \dots, N$ outside the operator $\mathcal{L}$ as in equation $(1)$.