5. Determine the convergence or divergence of the following series 3 «Σ(+)" (6) Σ (57)" n=0 η
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Solved in 1 steps
- 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)" n7. Find the value of p for which the series ) (-3)"(p – 5)" is convergent. n=15. 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=0
- 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=1S (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]Which one of the following sequence or series converges 1-3...5...(2k–1) 10k k²+3k-5 (D) Ek=2 k(ln k)² 1 (A) (B) Σ-0- 1)". (C) En=1 3k2–2k–1 =1 3k²-2k-1 (E) none of (A) - (D)
