- #1

Unconscious

- 74

- 12

##\lim_{N\to\infty}\frac{\sum_{p=1}^N T_{4N} \left(u_0(N)\cdot \cos\frac{p\pi}{2N+1}\right)}{N}##

is equal to 0?

In the expression above ##T_{4N}## is the Chebyshev polynomials of order ##4N##, ##u_0(N)\geq 1## is a number such that ##T_{4N}(u_0)=b##, with ##b\geq 1## fixed.

I tried to write ##T_{4N}## in its polynomial form, and to expand in series the terms ##\cos^k##, trying to reach a geometric series that would simplify everything to me in a chain, but still remains an abomination.