The sum of the first n natural numbers is given by 1+2+3...+n=(1/2)*n*(n+1). If the sum of n natural numbers is 55, what is the value of n?

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The sum of the first n natural numbers is given to be 55. The formula to calculate this sum if (1/2)*n*(n + 1)

To find the value of n if the sum is 55, equate the formula for n to 55 and solve for n.

(1/2)*n*(n + 1) = 55

=> n^2 + n = 110

=> n^2 + n - 110 = 0

=> n^2 + 11n - 10n - 110 = 0

=> n(n + 11) - 10(n + 11) = 0

=> (n - 10)(n + 11) = 0

=> n = 10 or n = -11

As n = -11 is not an acceptable value, we can eliminate that.

The required value of n is 10

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