Problem 3 Determine the convergence or divergence of each series below. Identify the test used. a\sum_(n=0)^(\infty ) (2n+1)/(3n+2) b\sum_(n=0)^(\infty ) 9^(-n) c\sum_(n=1)^(\infty ) ((1)/(n^(2))-(1)/(n)) d\sum_(n=1)^(\infty ) (1*3*5*dots*(2n-1))/(2*4*6*dots*(2n)) e\sum_(n=1)^(\infty ) ((3n-1)/(2n+5))^(n) f\sum_(n=1)^(\infty ) ((-1)^(n+1)\sqrt(n))/(\root(4)(n)+2) g\sum_(n=1)^(\infty ) (n!)/(e^(n^(2))) h\sum_(n=1)^(\infty ) e^(-(n)/(3))
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Identify the test used. a) $\sum_{n=0}^{\infty} \frac{2n+1}{3n+2}$ b) $\sum_{n=0}^{\infty} 9^{-n}$ c) $\sum_{n=1}^{\infty} \left(\frac{1}{n^2} - \frac{1}{n}\right)$ d) $\sum_{n=1}^{\infty} \frac{1*3*5*...*(2n-1)}{2*4*6*...*(2n)}$ e) $\sum_{n=1}^{\infty} Show more…
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8.) For problem (a)-(i), determine whether each series converges or diverges. Identify the test (or tests) that you use. Be sure to state the conditions of the test. There may be more than one correct way to determine convergence or divergence of a given series. Just a reminder of the test we have studied (or will study): (a) Geometric Series Test (b) Nth term Test for Divergence (c) Direct Comparison (d) Limit Comparison (e) Ratio/Root Test (f) Alternating Series Test (g) p-series Test (h) Integral Test (a) ∑_{n=1}^{∞} 1/n^{3/2} (b) ∑_{n=1}^{∞} n^2/(2n^2 + 1) (c) ∑_{n=1}^{∞} 3^n/n! (d) ∑_{n=1}^{∞} (e/π)^n (e) ∑_{n=1}^{∞} (n^2 + 1)/(2n^3 - n + 5) (f) ∑_{n=1}^{∞} ((3n + 1)/(4 - 2n))^{2n} (g) ∑_{n=1}^{∞} 5/4^n (h) ∑_{n=1}^{∞} ((-1)^n * 3)/(4n + 1) (i) ∑_{n=1}^{∞} cos(nπ)/n
Adi S.
Test for convergence: (a) $\sum_{n=1}^{\infty} \frac{1}{n^{2}+1}$ (b) $\sum_{n=1}^{\infty} \frac{n}{4 n^{2}-3}$ (c) $\sum_{n=1}^{\infty} \frac{n+2}{(n+1) \sqrt{n+3}}$ (d) $\sum_{n=1}^{\infty} \frac{3^{n}}{n \cdot 5^{n}}$, (e) $\sum_{n=1}^{\infty} \frac{1}{5 n-3}$, (f) $\sum_{n=1}^{\infty} \frac{2 n-1}{(3 n+2) n^{4 / 3}}$
Sam S.
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