Government Elections

In the parliamentary elections of a certain country, a number of parties participated (the exact number is unknown). Every citizen who participated in the elections voted for one party.

For every positive integer k, let `d_k` denote the number of parties that received k or more votes. Prove that the sum `d_1+d_2+d_3+...` is equal to the number of citizens who voted in the elections.

Difficulty level (1 very easy - 10 very hard): 3

Topics:
Combinatorics -> Induction (Mathematical Induction)
Sources:
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