Test for convergence the series 00 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) 3D 0. 2.4.6 ... (2n + 2) 3.5.7 ... (2n + 3) -!(x> 0). (ii) E •..
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All possible value of x for convergence
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- a. Determine a suitable ?-series to compare with (the second equation) b. Do specify if you are using a common-sense comparison of two large-indexedterms of the series or if you are using the limit comparison of the ratio of the two terms.state whether the series converges or diverges and by which convergence test. Options: a. diverges-alternating series test b. converges ratio test c. converges alternating series test d. diverges integral comparison test e. diverges ratio test f. diverges alternating series test ∞∑n=1 1 n10 ---------- 6 + n11 ∞∑n=1 4n ------ n10 ∞∑n=1 n2·4n ------- n!Helping determining if the series converges
- 4. Determine whether the series converges or diverges by comparing it to a p-series. ∞ ln 1 + 18 n n n=1 PLEASE SHOW STEP BY STEP CLEARLY .(a) Find the radius of convergence of an(x − c)n. n=0 (b) Find a power series for ∞ d ∑ an(x − c)n, dx n=0 and determine its radius of convergence. (c) Find a power series for ∫ ( ∞) ∑ an(x − c)n dx, n=0 and determine its radius of convergence.Test the series for convergence or divergence. a) b) c)