4) Give an properties: example, if possible, of power series with the following (a)) centered at Zo=3i, with radius of convergence R = 7 (b) centered at Zo=1 and convergent for all z with Imz≤4, but divergent for all z with Im Z >4 centered at Zo=0 and convergent for all z with Rez = 8, but divergent for all other ZEC.
Q: (c) AB (d) |AB|
A: |A| = -15, |B| = 52, |AB| = -780Explanation:
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- Suppose that the series ax has radius of convergence 5 and (a) (b) 2 (an+b)xn n=1 n=1 (c) bn(x - 2)4n n=1 n=1 R = an(x-7) R = R = n=1 box has radius of convergence 9. Find the radius of convergence of the following series.Find the interval of convergence of the 6k series Lk=1 · 3Find the interval and radius of convergence for the power series x" n yn3"
- Determine the sum of the series 1 n(n + 2) n=1 if possible. (If the series diverges, enter 'infinity', '-infinity' or 'dne' as appropriate.)Determine the interval and radius of convergence for the following power series: 2" -(2x – 1)"-1 n=1 Lütfen birini seçin: '다, R = a. O b. 4 R = C. d. R = е. HIN M³8. Determine the radius of convergence and interval of convergence for the power series n(-1)" 4n n=1 -(x + 3)".
- What is the radius of convergence of the power series Ec (x/2)* if the radius of convergence of Ecg x* is R?Suppose that the series CnX" has radius of convergence 12 and the series 2 d,x" has radius of convergence 13. What is the radius of convergence of series (c, + dn)x" ?If > uk and > v% are convergent series, then > (uk + v%) and 2(uk – Vk) are convergent series and the sums of these series are - related by 2(uk + vk) = 2Uk + Uk k=1 k=1 00 00 00 >(uk – Vk) UR) = Luk – L Uk - k=1 k=1 k=1 Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary. 1 (a) k2 – 1 10k–1 k=2 8WI WI