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1451Alternating-Input Recurrence 1A sequence satisfies x (n+1) = 1/2 x n + c n, where c n = 1 on odd n and c n = 3 on even n. Assuming any starting value x 1, what are the limits of the even and odd subsequences?数学简单数值题未尝试免费1456Contracting Second-Order Limit 1A sequence obeys x (n+2) = 1/4 x (n+1) + 1/5 x n + 3. If the sequence converges, what must its limit be?数学简单数值题未尝试免费1462Spaced-Pole Telescoping Series 2Evaluate the infinite series sum (n=1) inf 1 / [(4n+1)(4n+1+4)].数学简单derivation未尝试免费1466Repeating-Block Power Series 1Let a n repeat the block [1, 0, 2] forever. Evaluate sum (n=1) inf a n * (1/3) n.数学简单数值题未尝试免费1467Repeating-Block Power Series 2Let a n repeat the block [2, -1] forever. Evaluate sum (n=1) inf a n * (1/4) n.数学中等derivation未尝试免费1469Repeating-Block Power Series 4Let a n repeat the block [1, 2, 0, 1] forever. Evaluate sum (n=1) inf a n * (1/2) n.数学困难derivation未尝试免费1470Repeating-Block Power Series 5Let a n repeat the block [4, -2, 1] forever. Evaluate sum (n=1) inf a n * (1/6) n.数学困难derivation未尝试面试订阅5850Alternating Geometric SumEvaluate the infinite series sum (n=0) inf 5 * (-2/3) n.数学简单数值题未尝试免费5851Telescoping Log Partial SumFind the value of the partial sum S N = sum (n=1) N ln(1 + 1/n), and state whether the full series converges.数学简单数值题未尝试免费5852Nested Radical Fixed PointA sequence is defined by x 1 = 1 and x (n+1) = sqrt(2 + x n). Assuming it converges, find its limit.数学中等数值题未尝试免费5853Radius of Convergence via Ratio TestDetermine the radius of convergence of the power series sum (n=1) inf (3 n / n) x n.数学中等数值题未尝试免费5854Reciprocal Product SeriesEvaluate the infinite series sum (n=1) inf 1 / (n(n+1)).数学简单数值题未尝试免费5855p-Series Convergence ThresholdFor which of the following exponents p does the series sum (n=1) inf 1/n p converge: p = 1/2, p = 1, p = 3/2, p = 2? List all values for which it converges.数学简单数值题未尝试免费5856Compound-Limit ExponentialEvaluate the limit of the sequence a n = (1 + 3/n) n as n -> inf. Give the exact value and a decimal to three places.数学中等数值题未尝试免费5857Arithmetico-Geometric SeriesEvaluate the infinite series sum (n=1) inf n * (1/2) n.数学中等数值题未尝试免费