Consider a sequence {an }nen such that an 2 0, {an }nEN is decreasing and lim an = 0. Consider s, = a1 - a2 + a3 - . .. + (-1)" an = n-+00 7Z E(-1)k-lak. k=1 . Show that the sequence {82n-1}neN = ($1, $3, $5, ...) is decreasing. . Show that the sequence {san}neN = ($2, $4, $6, ...) is increasing. . Show that $2n-1 2 sk for any k 2 2n - 1 (any odd term is an upper bound for all terms after that). . Show that $2n