Jse the limit theorems to prove that the following sequences converge. 15n2 – 6 sin(2n + 1). bn n +1 n; n + 2 9n dn (n +8)!" An :- Cn = n – 5n2 - 1 n

Q: Prove that the sequence {sin n + cos n is bounded. =1

A: The given sequence is We have to prove that the sequence is bounded.

Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: Find the following infinite TM & α) Σ ntl (-3) n+1 A-1 5" infinite sums. 2 b) Σ (2n+1)(2n+3) n=1

A: Step 1: Step 2: Step 3: Step 4:

Q: 00 n-1/2 6 + cos (n) A) diverges B) converges

A: Given series is: ∑n=1∞n-126+cos2n

Q: 3. Express 0.7 + 0.007 + 0.00007 + ... using sigma notation. A) Σ0.7)1001 B ) Σο0.7)100" C)…

A: By using the formula of geometric progression and Arithmetic progression we can solve this question.

Q: аn +1 Suppose that 1 as n → o. Find the radius of convergence. an n2n E an( – 36)"x²n n=1

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Q: Let an (2n³ + 1) sinn n² +1 (1) Does the sequence (2) Does the series n=1 n² + 1 (2n³ + 1) sinn n¹ +…

A: Here we have given a sequence  where,

Q: Use the appropriate error theorem to find the sequence bn in terms of N, such that +00 1 1 IE(-1)".…

A: Since you have asked multiple questions, we will solve the Question (i) for you. If youwant any…

Q: 4. Prove that 12 does not converge uniformly on S = [1,∞). Hint: Use Lemma 17.5 from Bartle and the…

A: let us consider the series by f_n(x) fn(x) =∑1∞x2n2 we have∑1∞x2n2≤1n2 limn→∞fn(x)=f(x)=0 This…

Q: 27 n + 191 The sequence tan 9 n + 169 n=1 O converges to 3 O converges to 6. O diverges converges to…

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Q: x[n] is shown in the figure below. Sketch the sequences x₁ [n] and x₂ [n] specified as: x₁ [n] =…

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Q: um the following: (pa-py-kak k=0

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Q: For the sequence an = n cos n n² +1

A: given a sequence

Q: Mark all of the sequences that are monotonic. {sin(n²)}1 In(n) l n P (2) n=1 { n=1 [n² − 1] n² + 1…

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Q: Use the definition of convergence to prove lim COS n 72-00 n²n+1 = 0 || -

A: