Sum of numbers $2 + 2^{2} + 2^{3} + 2^{4} + 2^{5}$ is

62

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64

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60

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66

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Solution

The correct option is A $62$
Since, $2 + 2^{2} = 2^{3} - 2$
$2 + 2^{2} + 2^{3} = 2^{4} - 2$
$2 + 2^{2} + 2^{3} + 2^{4} = 2^{5} - 2$
In general, the sum of the powers $2$ , $2^{2}$ , $2^{3}$ and so on , is equal to $2$ subtracted from the next power to the last.
$∴ 2 + 2^{2} + 2^{3} + 2^{4} + 2^{5}$
$= 2^{6} - 2$
$= [(2 \times 2 \times 2) \times (2 \times 2 \times 2)] - 2$
$= [8 \times 8] - 2$
$= 64 - 2$
$= 62$

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