再请证明

∑²_i=1∑ⁿ_j=1 r_i(j) is exactly 2ⁿ⁺¹ - 2

证明如下：
∑²_i=1∑ⁿ_j=1 r_i(j) = ∑²_i=1∑ⁿ_j=1 2^n-j = ∑²_i=1(2⁰ + ... + 2^n-1_{) = (}2¹ + ... + 2ⁿ) = 2ⁿ⁺¹ - 2