3. ( Evaluate the given summation. Write the COMPLETE and NEAT solution. Messy answers will be considered wrong. Express your final answer in its simplest whole or rational number or expression. Box your final answer. 2n² Α. 2k 100 Β. Σ k(2n + 3) k=51 8 rt C ΣΣΣ t T=0 t=0_s=1 Κ=1
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- What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?On a sketch of y=ex, represent the left Riemann sum with n=2 approximating ∫2 3 e^x dx. Write out the terms of the sum, but do not evaluate it: On another sketch, represent the right Riemann sum with n=2 approximating ∫2 3 e^x dx. Write out the terms of the sum, but do not evaluate it:I got confused halfway and I emailed my professor except he wasn't much help with this problem. The question is: Consider the function f(x)=(x^2)/4+6. In this problem you will calculate ∫ [4,0] (x^2/4+6)dx by using the definition --> ∫[b,a] f(x)dx =lim(n→∞) ∑ni=1 f(xi)Δx. The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval. Calculate Rn for f(x)=(x^2)/4+6 on the interval [0,4] and write your answer as a function of n without any summation signs. You will need the summation formulas from your textbook. A) Rn = B) limn--> inf Rn =
- (a)analytically (b) For n=5, calculate by applying Simpson's 1/3 and 3/8 rule together. Analytical Also get the actual error using the solution.If the $n$ th partial sum of a series $\sum_{n=1}^{\infty} a_{n}$ is\[s_{n}=\frac{n-1}{n+1}\]find $a_{n}$ and $\sum_{n=1}^{\infty} a_{n}$answer both letter C & D c) Calculate the left and right Riemann sums for the given value of n. d) the fist image.
- If the $n$ th partial sum of a series $\sum_{n=1}^{\infty} a_{n}$ is $s_{n}=3-n 2^{-n}$ find $a_{n}$ and $\sum_{n=1}^{\infty} a_{n}$Even though you make series 6+18+54+162+486 what is the series in summation notation A. 5 ∑ k=1 6(3)^k B. 5 ∑ K=1 6(3)^k-1 C. 5 ∑ K=1 3(6)^k-13). Express the series as a rational function. ∞ n = 1 1 x5n PLEASE SHOW STEP BY STEP CLEARLY .
- Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Then compute the corresponding errors EL, ER, ET, and EM. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) 1 20xex dx 0 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, EL and ER are decreased by a factor of about _______ , and ET and EM are decreased by a factor of about ________?A) The fraction b/a may be written as b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power series expansion ln(1+z)= z + z^(2) / 2+ ⋯) , valid for |z|<1 , to find approximate expression for the inductance when b−a is much less than a. Express your answer in terms of the variables N , I , h , b , a , and appropriate constants. L = ? B) Compare results with this L = μ0*N^(2)*A / 2πr .(a) Using fourth order Runge Kutta method with one step copute y(0.1) to five place of decimal if y'=0.31+0.25y+0.3t\power{2} y=0.72 when t=0. (b) Find the sum to infinity of the series 1-3x+5x\power{2}-7x\power{3}+....∞ where 0<|x|<1