5. True or False? You do not need to prove your answers (but know how you would prove them!). e) If (an) is Cauchy and p is a number such that for all k ∈ N, |ak − p| < 1/2, then (an) converges to a limit L that lies in the interval [p − 1/2, p + 1/2]. f) If (an) is Cauchy and p is a number such that for infinitely many values of k, |ak − p| < 1/2, then (an) converges to a limit L that lies in the interval [p − 1/2, p + 1/2]. g) Suppose (an) has limit 4 and (bn) has limit L and that bn > an for infinitely many values of n. Then L > 4.

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Q: use SERIES to evaluate the limits

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A: See the attachment

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A: For complete solution kindly see below step.

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Q: (e) $₁ = 5 and Sn+1 = √√4s +1 for n ≥ 1.

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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.