# Determine convergence or divergence of the series a 4

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14. Determine convergence or divergence of the series.
a k = k 3 + 2 k + 3 k 4 + 2 k 2 + 4 ,b k = 1 k lim k →∞ a k b k = lim k →∞ ( k 3 + 2 k + 3 k 4 + 2 k 2 + 4 ) ( k 1 ) = lim k →∞ k 4 + 2 k 2 + 3 k k 4 + 2 k 2 + 4 = 1 > 0 k = 1 ( 1 k ) diverges k = 6 k 3 + 2 k + 3 k 4 + 2 k 2 + 4 diverges Limit Comparison 26. Estimate the error in using the indicated partial sum n S to approximate the sum of the series.
28. Estimate the error in using the indicated partial sum n S to approximate the sum of the series.
Section 8.4 2. Determine whether the series is convergent or divergent.
2 1 2 ( 1) k k k lim k →∞ a k = lim k →∞ 2 k 2 = 0 a k + 1 a k = ( 2 ( k + 1 ) 2 ) ( k 2 2 ) = 2 k 2 2 ( k 2 + 2 k + 1 ) < 1 ¿ > a k + 1 ≤a k for all k≥ 1 ¿ > converges Alternating Series Test 4. Determine whether the series is convergent or divergent.
10. Determine whether the series is convergent or divergent.