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.
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.
Here $a=2, r=2$ and $n=10$
Using the sum formula $S_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$
We have $S_{10}=2\left(2^{10}-1\right)=2046$
Hence, the number of ancestors preceding the person is $2046$
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