Real Analysis help! Can you explain clearly what you are doing step by step!
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Real Analysis help! Can you explain clearly what you are doing step by step! Determine whether...
i. Explain why this definite integral is an improper
integral.
ii. Determine if this improper integral converges or
diverges. Be sure to treat the improper integral with appropriate
mathematical rigour. Simply treating the improper integral as if it
was a proper integral will result in zero marks. Furthermore, make
sure you clearly explain/justify each step in your limit analysis
working.
thanks for your answer, please give a clear
writing.
(b) Consider the definite integral 2 1 i. Explain why this...
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13 n8n (i) Determine whether ah diverges. If the sequence converges, find its converges or limit. o0 (ii) Determine whether r diverges. Justify your ansv swer an Converges o n-1 (b) Consider the series (2n)! 2 (n!) and determine whether it converges or diverges. Justify your answer IM8 8
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13...
1. Determine whether each of the series converges absolutely, converges diverges. State clearly the test you use in your work. conditio 17 o) In(In(n)) n , In(n) 3" p) n+1 g) /n r)
1. Determine whether each of the series converges absolutely, converges diverges. State clearly the test you use in your work. conditio 17 o) In(In(n)) n , In(n) 3" p) n+1 g) /n r)
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine whether {an} converges or diverges. If the sequence converges, find its lmit (ii) Determine whether diverges. Justify your answer an COnverges or n-1 (b) Consider the series (2n)! 2" (n!)? n=1 and determine whether it converges or diverges. Justify your answer
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n...
6. Determine whether each series converges or diverges by using an appropriate series test. Clearly indicate the series test used and show all work. (8 points each) (-1)"(n-1) a. 2n=1 ( Converges / Diverges ) by 72 b. En=2 n (Inn)* ( Converges / Diverges ) by
Use the integral test to determine whether the series converges. Show all work to justify your answer. vands n=1 Select one: O A. diverges O B. converges
Can someone please help me answer these! I will
rate!:):)
Determine whether the series converges or diverges. 1 5 5. Σ 9. Σ 29. ✓k² tk Σ arctan(k) 1+k? In Exercises 43-54, if possible, use the basic divergence test to decide that the series diverges. If this test doesn't apply, explain why. 45. (k²1 5K2
help me solve both questions please
QUESTION 8 Use the integral test to determine whether the series converges. 00 Ve2n_1 1 Σ n=1 diverges O converges QUESTION 9 Use the ratio test to determine if the series converges or diverges. nh n=1 Converges Diverges
I need help in determining whether the series converges or diverges. If it converges, I need to determine what it converges to, or I need to explain why I can't determine what it converges to. e"l 7t e"l 7t
2.0, so in the contention, butun she 3. (10), 10, 10) For each series, determine whether it converges absolutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. can reduce res conditionally 2