# notation for this summation

I have a summation of the product of two variable like this $$v_{j}f_i$$ where $$j=1,2,\dots,d,d+1,\dots, 2d,\dots, nd$$ and after each $$d$$ step $$i$$ changes from $$1$$ to $$n$$, is my notation following correct in this situation?

$$\sum_{j=1}^{nd}\sum_{i=1}^{n} v_j f^{(i)}?$$

what I mean is I want $$(v_1+\dots+v_d)f^{(1)}+(v_{d+1}+\dots+v_{2d})f^{(2)}+\dots$$

So you have $$\begin{split} S &= (v_1+\dots+v_d)f^{(1)}+(v_{d+1}+\dots+v_{2d})f^{(2)}+\dots \\ &= f^{(1)}\sum_{k=1}^d v_k + f^{(2)}\sum_{k=d+1}^{2d} v_k + \ldots \\ &= \sum_{i=0}^n f^{(i+1)}\sum_{k=di+1}^{d(i+1)} v_k \end{split}$$