Concept explainers
The proof of the
Answer to Problem 52E
If the integral converges, then the second inequality puts an upper bound on the partial sums of the series.
Explanation of Solution
Given information:
The Integral Test (Theorem 10) for N = 1
Formula used:
Calculation:
For N=1 and
If the integral diverges, it must go to infinity, and the first inequality forces the partial sums of the series to go to infinity as well, so the series is divergent, If the integral converges, then the second inequality puts an upper bound on the partial sums of the series, and since they are a non-decreasing sequence, they must converge to a finite sum for the series.
Conclusion:
If the integral converges, then the second inequality puts an upper bound on the partial sums of the series
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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