Ancestors A person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of a person’s ancestors in generations?
The total number of a person’s ancestors in generations.
A person has two parents, four grandparents, eight great-grandparents, and so on.
Show that the number of ancestors in subsequent generations form a geometric sequence. And find partial sum of first terms of this generation.
Ratio of ancestors in second generation to first generation is .
Ratio of ancestors in third generation to second generation is .
This proves that the ancestors in subsequent generation form a geometric sequence with first term, and common ratio, .
The sum of first terms of this sequence is,
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