Determine convergence or divergence of the series using ratio or root test. Clearly identify the test used. (b) IM8iM8 n=2 (Inn)n (n!) (c) nn n=1 n και Στοι (3) (d) n=1 (e) n=0 ∞ (f) Σ n=0 2η - 3η – 5, 4n 3n+1
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- Find the power series for f(x) = 8x³ (1-x4)² 2 Hint: First, find the power series for g(x) = 1x41 (Express numbers in exact form. Use symbolic notation and fractions where needed.) 8 in the form S an. n=1 an = Then differentiate.Find the radius and interval of convergency of the power series (-1)" n=1 (2x - 1)" n5nThe power series (-1)" 3 2n+1 n=0 at x=-1 is equal to 3 1 3/2
- Determine whether the Ratio Test is inconclusive (that is, it fails to give a definite answer), conclusive (convergent), or conclusive (divergent) for each series. (=) E 1 n3 n = 1 O inconclusive conclusive (convergent) O conclusive (divergent) (b) E 3n n = 1 O inconclusive conclusive (convergent) O conclusive (divergent) (-5)^ – 1 Vn n = 3 O inconclusive O conclusive (convergent) O conclusive (divergent) (d) Š IVñ n=11 + n2 O inconclusive conclusive (convergent) O conclusive (divergent)(6) Determine if the alternating series converges Σ(-1)^n +1. n=2Question1: a) Find a power series representation of 1/(3-2x). b) Find a power series representation of 1/(3-2x)^2. Hint: part (a) should help with part (b)
- Ans./ Diverged Q5/ For the following series :- 1 (x- 2), (x – 2)2 f(x) = 2 (x – 2)" 2n+1 4 8 ... .....+ (-1)". Find :- a- Values of (x) that make series converged b- The sum of series Ans/ a) 0Find a power series representaton for f(x) = 1/(5+2x)32n + 4 (8) Does the series converge or diverge? Justify your answer. TAn+1 n=1Using 1/(1-x), find a power series for f(x)= 3/(2x+5) and its interval of convergence. Write step by step.Determine the series of the functions below. Write out the first four terms of the series a) f(x) = 8 e 2x b) h( x ) = e! ×^232n +4 „An+1 Converge or diverge? Justify your answer. (8) Does the series n=1SEE MORE QUESTIONS