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- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+8. Determine the radius of convergence and interval of convergence for the power series n(-1)" 4n n=1 -(x + 3)".H.W 1/For the following series: - (x- 2). (*-2)2 (x- 2)" 2n+1 f(x) = ..+ (-1)". 4. Find: - a Values of (x) that make series converged b- The sum of series
- 7.) Find the interval of convergence of the power series n=1 2" (x+2)" n5. Suppose that the power series E Cnx" converges when x = 3 and diverges when x = 6. Which of the following n=0 statements is certain to be true? (a) None of these statements is certain to be true. (b) Σ Cn(-4)" is convergent. n=0 (c) Σ Cn(-3)" is convergent. n=0 (d) > Cn(-2)" is convergent. n=0 (e) 2 Cn(-6)" is divergent. n=07. Find the value of p for which the series ) (-3)"(p – 5)" is convergent. n=1
- 30. Write the first five terms of the power series * (-1)"(x – 2)" n=1 5" a. (x- 2) (x-2), (x- 2) (x – 2)* , (x-2)³ 53 52 54 55 b. (x– 2) (x – 2)² (x- 2) 52 (x – 2)* (x- 2)5 54 53 55 (x- 2), (x-2) (x- 2), (x-2) (x-2)5 с. 52 53 54 55 d. (x- 2) , (x-2)² (x-2) (x-2) (x-2) 52 53 54 55 (x-2) (x-2)2 е. (x-2)3 (x- 2)* (x– 2)° 52 53 54 55 inQ3. Find the sum of the following series. (-1)") + 5n 2n n=0 00 \2n 2/(n+1), n=1 Q4.10. Find the interval of convergence and the radius of convergence of the power series • (x- 4)" n=1 n-9"
- 7. Find the radius of convergence and the interval of convergence of the following power series. (-5)" (x – 1)" n+3 n=1Suppose that the power series Σan(x-6) n=1 converges at x = 9. At which of the following points MUST it also converge? (i) x = 8 (ii) x = 6 (iii) x = 3 (A) none of them (B) all of them (C) (i) and (iii) only (D) (i) and (ii) only (E) (ii) only (F) (i) only (G) (ii) and (iii) only (H) (iii) onlyS (x+7)" convergent range of series n=1 Select one: a. (-1-7,1-7] (+-1,1-7) O * [T-1,1-7] O d. [-1-7,1-7) е. * (7-11-7]