Lost in Addition

Find the number between 1 and 49 (inclusive) such that the sum to the left of it is equal to the sum to the right of it.

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Note: For example, between 1 and 8, 6 would be the answer, as the sum of the numbers to the left of 6, which is \(1+2+3+4+5=15,\) is equal to the sum of the numbers to the right of 6, which is \(7+8=15.\)


Bonus: Generalize it for any set of numbers from \(k\) to \(n\) with proof.

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