Determine whether the improper integral converges or diverges, and find the value of each that converges.
∫^[infinity]_1 1/x^^0.999 dx

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.