Use the Weierstrass M-test to show that the series of functions xn n! converges for rwhere...
3. (a) Use the Weierstrass M-test to show that the series Σ V1 – cos2 (nx) 1+ n2 n=0 represents a continuous function on R.
5. Using the Weierstrass M-Test, show that a sin (3) converges in all n=1 of R. 6. Determine the type of convergence of fn (x) as n - as for fn (2) -nac ve Te [0, x). 7. Determine if fn (x) = converges pointwisely or uniformly on R. 8. Consider fn (x) = x"on (0,1), prove that { fn} converges pointwisely. 9. Prove that the sequence fn (2) for 2 € 2,) converges uni- formly. 10. Determine the type...
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...
Use the Ratio Test to determine if the following series converges absolutely or diverges. (-1; n(n+2)! n=1 Since the limit resulting from the Ratio Test is (Simplify your answer.) the Ratio Test is inconclusive. the series diverges. the series converges absolutely.
Use an appropriate test to determine whether the series given below converges or diverges. Show all work needed to support the conclusion of convergence or divergence. State all tests used. Give any values of "r" or "p" or limits used. (n+7)(n+3) n = 1 Select the correct choice below and fill in the answer box to complete your choice. O A. The series converges. OB. The series diverges.
please show all work Use any method to determine if the series converges or diverges. Give reasons for your answer. n! Σ (2n + 3)! n=1 Select the correct choice below and fill in the answer box to complete your choice. O A. The series diverges because the limit used in the nth-Term Test is OB. The series converges because the limit used in the Ratio Test is O c. The series converges because the limit used in the nth-Term...
Question 5 Use the ratio test to determine if the series converges or diverges. ne-7n n=1 Diverges O Converges Question 6 Use the root test to determine if the series converges or diverges. DO Σ n n=1 n6 Diverges Converges
7. Use the ratio test to determine whether the series converges or diverges: n!
7.29. Use the Weierstraß M-test to show that each of the following series converges uniformly on the given domain: zk (a) Σ on D[0,1] k2 (c) zk+ on D(0,r) where 0 <r <1 1 (b) Σ on {z E C : |Z| > 2} izk ko
an converges. 6. We want to use the Integral Test to show that the positive series All of the following need to be done except one. Which is the one we don't need to n=1 do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = an for all n. (b) Show that ſi f(x) de converges. (C) Show that lim f(x) dx exists. t-00 (d) Show that lim sn exists....