7. Show that Σο.nafm + n)-p converges if and only if p > 2, (Hint: Use triangular partial sums.) 7. Show that Σ...
4. Show that for any p > 1. This shows that a p-series converges for any p > 1 р— 1 1 to an improper integral Hint: Compare Notice that the sum you need to compare n=2 2, not n 1. Find a function f(x) such that on the interval n - 1,n]. < f(x) starts at n = You might want to draw a picture to help visualize it. Think about right-hand Riemann sums with Ax= 1.
Problem 2 Show that if the sequence of numbers (an)n-1 satisfies Inlan) < oo, then the series In ancos(nx) converges uniformly on [0, 27). This means, the partial sums Sn(x) = ) ancos(nx) define a sequence of functions {sn} = that converges uniformly on [0, 271]. Hint: First show that the sequence is Cauchy with respect to || · ||00.
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
1) Show that Σ COSNTT N converges/diverges. N-1 2) Find the sum Σ e-N N-1 00 n 3) Show that Σ converges/diverges n=1 + 1
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
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help calculus II
Spring 2019 ) (A) Show that Σ (-1)+7-2 converges using the Alternating Series Test. Be sure to say what the AST requires for convergence. Hint: The derivative of ()7 is Math 2502 Test 4 r(z)=菰11-r.7ア, which 一疋 2, 00 2V-27)' which has domain (2,oo).
Spring 2019 ) (A) Show that Σ (-1)+7-2 converges using the Alternating Series Test. Be sure to say what the AST requires for convergence. Hint: The derivative of ()7 is Math 2502...
11.7 Inverse of an upper triangular matri. Suppose the n × n matrix R is upper triangular and invertible, i.e., its diagonal entries are all nonzero. Show that R1 is also upper triangular. Hint. Use back substitution to solve Rsk-en for k 1, , n, and argue that (sk)i -0 for i > k.
11.7 Inverse of an upper triangular matri. Suppose the n × n matrix R is upper triangular and invertible, i.e., its diagonal entries are all nonzero....
Please write it clearly and show every step
ere Cesaro Sumrnability. Given an infinite series Σ an let Sn be the sequence of partial sums and let 5 Tt A series is Cesaro-surmable if linn-troƠn exists (and is finite). and this limit is called the Cesàro sum (a) Given the series 2n-1 n' s", hnd 8m and Ơn for any 1. and find the Cesaro sum of ΣΥ_1)". (b) Find the Cesàro sum of Here you may use the fact,...
Use the Weierstrass M-test to show that the series of functions xn n! converges for rwhere r is any fixed positive real number. (Hint: Use the ratio test.)
1. (a) (3 pts) Show that the sequence defined by p. = 1/n converges linearly to p = 0. (b) (7 pts) Generate the first five terms of the sequence for using Aitken's Amethod. PL