MathDB

17

Part of 2020 LIMIT Category 2

Problems(1)

triangle with sidelengths 4n^2, 4n^4+1 , 4n^4-1 , angle limit wanted

Source: LIMIT 2020 Cat 2 Objective P17

6/9/2020
Let ana_n denote the angle opposite to the side of length 4n24n^2 units in an integer right angled triangle with lengths of sides of the triangle being 4n2,4n4+14n^2, 4n^4+1 and 4n4−14n^4-1 where n∈Nn \in N. Then find the value of lim⁡p→∞∑n=1pan\lim_{p \to \infty} \sum_{n=1}^p a_n (A) π/2\pi/2 (B) π/4\pi/4 (C) π\pi (D) π/3\pi/3
limitTriangleanglecalculus