How many of the first n natural numbers must be added to produce a sum of 4,950.

To solve this problem, we need to use the formula for the sum of the first n natural numbers, which is n*(n+1)/2.

We set this equal to 4950 and solve for n:

n*(n+1)/2 = 4950 n^2 + n - 9900 = 0

This is a quadratic equation, and we can solve it using the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). In this case, a = 1, b = 1, and c = -9900.

n = [-1 ± sqrt((1)^2 - 41(-9900))] / (2*1) n = [-1 ± sqrt(1 + 39600)] / 2 n = [-1 ± sqrt(39601)] / 2 n = [-1 ± 199] / 2

We discard the negative solution because n must be a natural number, so n = (199 - 1) / 2 = 99.

Therefore, the first 99 natural numbers must be added to produce a sum of 4950.