Question: Show code and explain each step Show code and explain each step. Use the MATLAB command format long e to display your numerical results with
Use the MATLAB command "format long e" to display your numerical results with 15 digits of precision Consider the Riemann zeta function(s) = EK=11/k*. The value of is approximated by the succession of partial sums, and is denoted by the error of said approximation. -Consider the function t ++* with x > 1, to show that Uk > 2. .t-* dt = (k-1)** Vk 2. Induction is not required. -Show the following dimension for the error 0 Sens (k-1)*n*-1" Use this bound to obtain n E N that guarantees an error less than 10 whenx = 1.1, not you are asked to approximate (x). - Include the implementation of the routine "[2, 2p] = zetaRieman(x,n)", in MATLAB. in which returns the approximation of (x) through the summation Sn, which is calculated from two different ways: 2 is calculated by accumulating from the left, that is, 1 1 2L = (... (--((1+y)+5+) +- tema Zr is calculated by accumulating from the right, that is, 2x = (1 + (x+ +++ 1 (n-1)* +)) -Using other techniques it is known that the exact value ofg(2) = 1/6. Use your routine to approximate 3(2) with n = 108,109, show the obtained values of Z and Zg. Explain clearly and concise the results obtained. - In a table show the results obtained by your routine to approximate (4)with n = 10P.p = 2,3,...,8. Briefly and concisely comment on the results obtained. Ruse the MATLAB command "format long e" to display your numerical results with 15 digits of precision. Consider the Riemann zeta function(s) = EX=11/k*. The value of is approximated by the succession of partial sums; and is denoted by the error of said approximation. -Consider the function t ++-* with x > 1, to show that Vk 2 2. **dt sa-vx, Vk 22. Induction is not required. -Show the following dimension for the error 0 Sens (k-1)* nx-1" Use this bound to obtain n N that guarantees an error less than 10 whenx = 1.1, not you are asked to approximate (x). -Include the implementation of the routine "[2,Zx] = zetaRieman(x,n)", in MATLAB, in which returns the approximation of(x) through the summation Sn, which is calculated from two different ways: Z is calculated by accumulating from the left, that is, 1 1 22 2z=--((1+2+) + +++ ++ Zr is calculated by accumulating from the right, that is, 2x = (1+(2+ 1 + + (n-1)* + (n-1)3 + ) - +) - Using other techniques it is known that the exact value ofg(2) = 1/6. Use your routine to approximate (2) with n = 108, 109, show the obtained values of Z and Zg. Explain clearly and concise the results obtained. -In a table show the results obtained by your routine to approximate (4) with n = 10P, p = 2,3,...,8. Briefly and concisely comment on the results obtained
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