A boy added all natural numbers from 1 to 12, | vedclass

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(B) The sum of the first $n$ natural numbers is given by the formula $S = \frac{n(n+1)}{2}.$For $n = 12,$ the sum is $S = \frac{12 	imes (12+1)}{2} =

Vedclass · Accepted Answer

$2$

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(B) The sum of the first $n$ natural numbers is given by the formula $S = \frac{n(n+1)}{2}.$For $n = 12,$ the sum is $S = \frac{12 	imes (12+1)}{2} = \frac{12 	imes 13}{2} = 78.$Let the number added twice be $x.$The new sum is the original sum plus the extra number: $S_{new} = S + x.$Given $S_{new} = 80,$ we have $80 = 78 + x.$Therefore,$x = 80 - 78 = 2.$The number added twice is $2.$

$A$ boy added all natural numbers from $1$ to $12,$ however he added one number twice due to which the sum became $80.$ What is the number which he added twice?

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