Strategy for Testing Series: Solutions
MAT V1102 – 004 Solutions: page 2 of 7 8. Since ex is a strictly increasing function, e1/n ≤ e for all n ≥ 1. Hence, we have e1/n n3/2 ≤ e n3/2 Since P en−3/2 converges (it’s a p-series with p = 3/2 > 1), the comparison test implies that P e1/nn−3/2 also converges. 9. If f(n) = (n+2)(n+3) (n+1)3 then f′(n) = (2n+5)(n+1)3 − 3(n2 +5n+6)(n+1)2 (n+1)6 = − n2 +8n+13
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