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 72. E(-1)K-lak. k=1 . Show that the sequence {s2n-1}nEN = ($1, $3, $5, . . .) is decreasing. . Show that the sequence {san }nEN = ($2, $4, $6, . . .) is increasing. . Show that son-1 2 sk for any k 2 2n - 1 (any odd term is an upper bound for all terms after that). . Show that 82n