90 for the Series a) 6) Cicale the first 4. fenmula S, Sz, S3, S, Sa fer write partial Sums. out for the kh parliel Sum. n22 C) find the Vaulue to the Serics. which converges.

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Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

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Q: 5. State

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Q: t Z an = 3+040+ 0 +O … Find $s, o Does the sesies converge ? H what is the sum ?

A: We have the given series is ∑n=1∞an=3+0+0+0+... Here the first term a1=3 The second term a2=0 and…

Q: x V4 – x² + c - dx V4 – x2 2 arcsin 2 8 IN

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Q: Sequences, limits, Cauchy criterion. a) State the Cauchy condition: A sequence (x,) is a Cauchy…

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Q: Q9) Find the rule for the nth term (term an )of the following sequence: a) 2, 6, 18, 54, ... b)…

A: Since you have asked a multiple questions, we will solve the first question for you. If you want any…

Q: Using set-builder notation, identify the domain of the following functions p(x) = x q(x) = x - 5

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Q: Let DEIR, xn be a sequence in [DEIR+correction Proof: Suppose D is closed. To prove xn ED 6-t xnxx…

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Q: 12 71. (-5-81) 1-4 1000

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Q: Show that if Sn and tn are both Cauchy sequences, then sn tn is also a Cauchy sequence.

A: Given that sn and tn are Cauchy sequences. how we have to show that product of two Cauchy sequence…

Q: Exercise 3. For a and b in R defined for 15, 2 by s we consider the Sequence Un = a + b Un-1 with Us…

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Q: Determine the values of the following sums: n-1 (a) z = (1 + i) k=0 n-1 (b) z = (1+i)k k=0

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Q: Hiw Find 7-transform for fCk) = la, k>o 11 wotes this sequence is called the Unil vamp" rC)じ。 Ans:…

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Q: Determine whether the nonincreasing sequence converges or diverges. 5) an 1 +V8n n A) Converges B)…

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Q: Find the indicated nth partial sum (Sn) of the arithmetic sequence 20.0190 a) 8, 20, 32, 44... n=10…

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Q: Let an be the number of sets S of positive integers for which > Fk = n, kES where the Fibonacci…

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Q: let be a sequence sit. 2 for oxaza2 12 then 6'mam=? 348

A: Let an be a sequence  such that for 0<a1<a2 an+1=an+an-12,n⩾2. Find limn→∞an.

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Q: Q.14) A sequence {()L a) converge to 3 b) diverge lecreasing

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Q: Calculate Reiren Sum by define tion Hexe C=2 D= 7

A: given f(x) = cx2 - Dx +1 in [2,3] here C = 2 and D = 7   we deduce here the  Riemann sumthe  left…