The sequence an=nsin(πn)a_n = n \sin(\frac{\pi}{n})an=nsin(nπ) is known to converge to π\piπ. Does the sequence bn=n2(1−cos(πn))b_n = n^2 (1 - \cos(\frac{\pi}{n}))bn=n2(1−cos(nπ)) converge?
Yes, to 000
Yes, to π2/2\pi^2/2π2/2
Yes, to π2\pi^2π2
No, it diverges