Do this by computing the sum for: n = 5, n = 10, n = 50 For each part create a v

Question

Do this by computing the sum for: n = 5, n = 10, n = 50 For each part create a vector n in which the first element is 0, the increment is 1 and the last term is 5, 10, or 50. Then use element-by-element calculations to create a vector in which the elements are 2^n/n~. Finally, use MATLAB's built-in function sum to sum the series. Compare the values to e^2 (use format long to display the numbers). Use MATLAB to show that the sum of the infinite series sigma_n = 1^infinity (9/10)^n/n converges to In 10. Do this by computing the sum for n = 10, n = 50, n = 100 For each part, create a vector n in which the first element is 1, the increment is 1 and the last term is 10, 50 or 100. Then use element-by-element calculations to create a vector in which the elements are (9/10)^n/n. Finally, use MATLAB's built-in function sum to sum the series. Compare the values to In 10 (use format long to display the numbers). According to Zeno's paradox any object in motion must arrive at the halfway point before it can arrive at its destination. Once arriving at the halfway point, the remaining distance is once again divided in half and so on to infinity. Since it is impossible to complete this process, Zeno concluded all motion

Explanation / Answer

Matlab Code

syms k x

S2 = symsum((0.9^k)/k,k,0,10)

Value of S2 = 2.11874

S3 = symsum((0.9^k)/k,k,0,50)

Value of S3 = 2.3017

S4 = symsum((0.9^k)/k,k,0,100)

Value of S4 = 2.302584

The value of ln(10) = 2.303

Hence as the number of terms are increasing, the sum is reaching closer to the value of ln(10)

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