How to find the sum of elements of all subsets of set {1,2,3,4,5..., n}? Why does each element appear 2 ^ (n-1) times?

∵ each element appears or does not appear in the subset, and there are two cases for each element
A set has 2 ^ N sets
In these sets, each element appears and does not appear in half, and each element appears 2 ^ n / 2 = 2 ^ (n-1) times

Let m = {a, B, C}, try to write all subsets of M and point out the proper subsets

The zero element proper subsets of set {a, B, C} are {a}, {B}, {C} for one element, and {a, B}, {a, C}, {B, C} for two elements. Therefore, all subsets of set {a, B, C} are Φ, {a}, {B}, {C}, {a, B}, {a, C}, and the proper subsets are Φ, {a}, {a}, {B}

Write all subsets of the set {a, B, C}
The set {a} has subsets
The set {a, B} has subsets
The set {a, B, C} has subsets
The set {A1, A2. An} has subsets

The set {a} has two subsets
The set {a, B} has four subsets
The set {a, B, C} has eight subsets
The set {A1, A2. An} has 2 ^ n subsets

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How to find the sum of elements of all subsets of set {1,2,3,4,5..., n}? Why does each element appear 2 ^ (n-1) times?