Question 22 < Σ n=2 as 10 Evaluate n2-1 10 First find the partial fraction decomposition of n2 - 1 10 Then n=2 n2-1 Note the partial sum is a telescoping sum. Write your answer for the sum as a reduced fraction.
Question 23 The Test for Divergence for infinite series (also called the "n-th term test for divergence of a series") says that: liman 70 → an diverges n=1 0; in that situation the series might 100 n=1 Notice that this test tells us nothing about an if liman converge or it might diverge. 5n3 Consider the series 3n3 + 6 00 The Test for Divergence tells us that this series: converges diverges O might converge or might diverge
Question 24 < > Given the series: 1 1 1 1+ ő + + 36 216 +... does this series converge or diverge? diverges converges If the series converges, find the sum of the series: 1 1 1 1+ + + + ... 6 36 216 (If the series diverges, leave this second box blank.)
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