Use MATLAB to show that the sum of the infinite series ∑ n = 1 ∞ 1 n 2 converges to p 2 /6. Do this by computing the sum for: (a) n =5, (b) n =50, (c) n =5000 For each part create a vector n in which the first element is 1, the increment is 1 and the last term is 5, 50, or 5,000 . Then use element-by-element calculations to create a vector in which the elements are 1 n 2 . Finally, use MATLAB’s built-in function sum to sum the series. Compare the values to p 2 /6. Use format long to display the numbers.
Use MATLAB to show that the sum of the infinite series ∑ n = 1 ∞ 1 n 2 converges to p 2 /6. Do this by computing the sum for: (a) n =5, (b) n =50, (c) n =5000 For each part create a vector n in which the first element is 1, the increment is 1 and the last term is 5, 50, or 5,000 . Then use element-by-element calculations to create a vector in which the elements are 1 n 2 . Finally, use MATLAB’s built-in function sum to sum the series. Compare the values to p 2 /6. Use format long to display the numbers.
Use MATLAB to show that the sum of the infinite series
∑
n
=
1
∞
1
n
2
converges to p2/6. Do this by computing the sum for:
(a) n=5, (b) n=50, (c) n=5000
For each part create a vectorn in which the first element is 1, the increment is 1 and the last term is 5, 50, or 5,000. Then use element-by-element calculations to create a vector in which the elements are
1
n
2
. Finally, use MATLAB’s built-in function sum to sum the series. Compare the values to p2/6. Use format long to display the numbers.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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