3. We will denote the set of positive integers by 23+. Let {33,1 }::1 be a sequence of real numbers. The alternating decomposition of {mnczl consists of the sequences {14,1}le and {JB.,.1};:l where Vii E Z+, An = 332111137: = 332m Prove the following lemma. Lemma: If 0 the sequences {14,3}le and {3,1}le are an alternating decomposition of a sequence {an}.:=1 0 {An i211 and {3,1}le are both convergent to the same limit THEN the sequence {3% }::1 is also convergent to this limit. Hint: Use the definition of limit. Note that the sequence {In}::1 is a general sequence of real number, unlike the other questions where sequences are positive