Fundamental Applied Maths Solutions Exclusive -

For ( n=1 ): coefficient ( 2 ) → matches sawtooth wave. ✔ At ( t=\pi/2 ): series gives ( 2 - 1 + 2/3 - 1/2 + \dots = \pi/2 ) (Leibniz series). ✔

Dirichlet conditions hold (finite jumps, finite extrema). fundamental applied maths solutions

Best‑fit line ( y = a + bx ) in the least‑squares sense. For ( n=1 ): coefficient ( 2 ) → matches sawtooth wave