1. Prove the following lemma: 8. Lemma A. Let {xn}1 be a sequence of real numbers. We define two new sequences {En}, and {On} as: n=1 n=1 n Sn=1 Vn E Zt, En = x2n) Vn E Z*, On = x2n-1 • IF the sequences {En}-1 and {On}=1 are both convergent to the same limit • THEN the sequence {xn}n=1 is also convergent. %3D1 Suggestion: Use the definition of limit.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.