Taking the square root of both sides:
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- c^2 = a^2 + b^2
- where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs. Substituting \(a = 6\) and \(b = 8\):
- c^2 = 6^2 + 8^2 = 36 + 64 = 100
- c = \sqrt{100} = 10
- Thus, the length of the hypotenuse is \(\boxed{10}\).**Question:
- To compute the sum \(\sum_{k=1}^{50} \frac{1}{k(k+1)}\), we can use partial fraction decomposition. We start by expressing \(\frac{1}{k(k+1)}\) in a simpler form:
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