A) Using a variation on the MCT show that for any non-increasing sequence (an) that is...

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A) Using a variation on the MCT show that for any non-increasing sequence (an) that is bounded below (an) converges and liman = glb(an) as a appraoches infinity. B) Similarly, use the MCT to show that for two non-decreasing sequences (an) and (bn) with bn an with (bn) convergent and limb = L that (an) must also converge and if liman = M then L > M. A) Using a variation on the MCT show that for any non-increasing sequence (an) that is bounded below (an) converges and liman = glb(an) as a appraoches infinity. B) Similarly, use the MCT to show that for two non-decreasing sequences (an) and (bn) with bn an with (bn) convergent and limb = L that (an) must also converge and if liman = M then L > M.