Show that each series in Exercises 61–66 is a telescoping series. For each series, provide the general term S, in its se- quence of partial sums and find the sum of the series if it converges. G-) 1 3 62. LR? + 3k +2 k k=1 k+2 k=1 1 1 1 63. Σ( 64. E 3k+1 k(k + 1)(k + 2) k=1 k=0 k 65. In k+1 1 66. In k2 – 1 k=1 k=2

Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

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Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: Evaluate the following telescoping series or state whether the series diverges. 1 1 Σ (n+1)* 102. 13…

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Q: 2. -2 +1- 16 + +

A: Given  (2)

Q: Part II: Recursion (10 pt.) 7. Give the first six terms (including the initial terms) of the…

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Q: 1 is convergent, and find its sum. Show that the series n(n + 1) n=1

A: we have to show that the given series is convergent and then we have to find the sum. ∑n=1∞1n(n+1)

Q: 5. Use Theorem 5.10 (Section 5.3 in Vol. 2 of OpenStax Calculus) for this problem. How many terms of…

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Q: Use Leibniz's method to find the sum of the series 2² +9² +16² +23² + ... +72² Suggestion: This is…

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Q: 8 2. If the series 4 5 16 32 +... converges, find its sum. Otherwise, say it diverges. 25 125 (A)…

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Q: Section 5: Taylor and Maclaurin Series Find the series for each. 24. Taylor series for f (x) = sin…

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Q: Evaluate th e relate series of each sequence. 1) -7,-5,-3,-1,1,3

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Q: Decide whether the given series are convergent or divergent. Show all your steps. (-4)3n a) 2n+1 n=1

A: Since you have asked multiple questions in single request.so we will be  answering only first…