In this problem we investigate how fast the partial sums SN = 15 + 25 + 35 + + N5 * of
Chapter 9, Problem 51(choose chapter or problem)
In this problem we investigate how fast the partial sums SN = 15 + 25 + 35 + + N5 * of the divergent series n=1 n5 grow as N gets larger and larger. Show that (a) SN > N6/6 by considering the right-hand Riemann sum for - N 0 x5dx with x = 1. (b) SN < ((N+1)61)/6 by considering the left-hand Riemann sum for - N+1 1 x5dx with x = 1. (c) limN SN /(N6/6) = 1. We say that SN is asymptotic to N6/6 as N goes to infinity.
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