(2) Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). ∞ ∞ (a) Σ n 2n (b) n2+1 n! n=1 n=1 ∞ շո (c) Σ 1+2n n=0 (α) Σ ΣΣΣ (e) (-1)+1 +1 n=1 n=1 n! 1 (f) 3n+2' n=1 (2n)!*
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Solved in 5 steps with 4 images
- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+(4) n=2 3n n3x5m (4) Determine if the series converges, enter CON when converging, and DIV when diverging. - J ............. +(-1)"+1( n+1 (x-5)" 2. Consider the power series n=1 4n n What is the center ? What is the interval of convergence
- 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)(-1)"(2x–3)" 2" (n+2020) 5. Determine the interval of convergence for the following power series: n=2020Let fn(x) be the following sequence (not series) of functions n2 fn(x) : (x2 + 7x + 6)n² +n (1) Is fn(x) convergent at x = 0? Why? (2) Is fn(x) convergent at x = (3) For what x is fn(x) convergent and for what x is it divergent? (4) What's the limit function -1? Why? f(x) = lim fn(x), and what's the domain of f according to your answer in the previous part?
- (x-6)" (14) Find the interval and radius of convergence for the power series 2 2" n=1+(-1)". (X-2)h 2 h+1 Fex) =Ź (x-2) _(x-2) --a. 4 Findea a.values of (x) that make series converged. la. The of series. Note with an explanation of the StePsConsider the series 2 (- 1)"(7x+ 2)". n=0 (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally?
- •(-1)"-1xn+1 Vn 22n+1 1. Find the radius of convergence and interval of convergence of the series: n=1 Radius of Convergence =, Interval of ConvergenceConsider the series 2 (- 1)"(5x + 8)". n = 0 (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally?