A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.

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Solution

To find number of ancestors, we will find the sum of $2, 2^{2}, 2^{3}, . . . . . .$

Number of ancestors $S_{10} = \frac{2 (2^{10} - 1)}{2 - 1}$

$= 2 (1024 - 1)$

$= 2 \times 1023$

$= 2046$

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A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his own.

To find number of ancestors, we will find the sum of 2,22,23,...... Number of ancestors S10=2(210−1)2−1 =2(1024−1) =2×1023 =2046

To find number of ancestors, we will find the sum of $2, 2^{2}, 2^{3}, . . . . . .$

Number of ancestors $S_{10} = \frac{2 (2^{10} - 1)}{2 - 1}$

$= 2 (1024 - 1)$

$= 2 \times 1023$

$= 2046$