1. Compute each of the following as best you can using SageMath. [ 1 dr [0.5]...

  

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1. Compute each of the following as best you can using SageMath. [ 1 dr [0.5] Hint: It is possible that you might have done something similar to some of these previously. :-) a. da [0.5] b. 3. Explain why the sum 2 [0.5] c. n=1 M8 2. Explain why the sum is what it is because the integral da is what it is. [2.5] Hint: A picture may be worth 103 words... Pay attention to the green (upper) dashed lines from 1 onward. dr [0.5] d.) has a finite value because the integral dr has a finite value. [2.5] Hint: Look at the picture iabove again. This time, pay attention to the red (lower, and between 0 and 1) dashed lines, especially from 1 onwards. 8 3. Explain why the sum has a finite value because the integral value. [2.5] Hint: Look at the picture iabove again. This time, pay attention to the red (lower, and between 0 and 1) dashed lines, especially from 1 onwards. [() Hint: Look at the picture yet again. This time, pay attention to the both the green (upper) and the red (lower) dashed lines from 1 onwards. 4. Explain why the limit lim k+x +1)] -In(k+ 5. Use SageMath to (approximately) evaluate lim k4x dr has a finite exists and is between 0 and 1. [2.5] [(2) - (+1)] (:) -In(k+1) as best you can. [0.5] 1. Compute each of the following as best you can using SageMath. [ 1 dr [0.5] Hint: It is possible that you might have done something similar to some of these previously. :-) a. da [0.5] b. 3. Explain why the sum 2 [0.5] c. n=1 M8 2. Explain why the sum is what it is because the integral da is what it is. [2.5] Hint: A picture may be worth 103 words... Pay attention to the green (upper) dashed lines from 1 onward. dr [0.5] d.) has a finite value because the integral dr has a finite value. [2.5] Hint: Look at the picture iabove again. This time, pay attention to the red (lower, and between 0 and 1) dashed lines, especially from 1 onwards. 8 3. Explain why the sum has a finite value because the integral value. [2.5] Hint: Look at the picture iabove again. This time, pay attention to the red (lower, and between 0 and 1) dashed lines, especially from 1 onwards. [() Hint: Look at the picture yet again. This time, pay attention to the both the green (upper) and the red (lower) dashed lines from 1 onwards. 4. Explain why the limit lim k+x +1)] -In(k+ 5. Use SageMath to (approximately) evaluate lim k4x dr has a finite exists and is between 0 and 1. [2.5] [(2) - (+1)] (:) -In(k+1) as best you can. [0.5]