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Question
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
Solution
Here, the ancestors of the person form the G.P. 2, 4, 8, 16, ........
Now, first term, a = 2
And, r = 2
∴ Number of his ancestors during the ten generations preceding his own,
\[S_{10} = 2\left( \frac{2^{10} - 1}{2 - 1} \right) = 2 \left( 1024 - 1 \right) = 2046\]
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