Let $0<a<1,b>1,c>1$ be some real numbers. Let $S$ denotes the sum of all the terms $d^{j},j=0,..,m$, where $d≥3$. Define $S_1,S_2,S_3,S_4$ be the partial sums of the terms $d^{j},j=0,..,m$ such that the union of all these sums is equal to $S$. Here partial sum means any sum of $h$ terms and not necessary conssecutive.
Then my question is: How one can choose those four sums to verify the inequality: $$S_1≥S_2+a+ b×S_3+ c×S_4$$