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Lebl-Basic-Analysis-I
· Problem 5.5.3
The Riemann Integral
Mathematics · improper-integrals-integral-test
Problem
a) Estimate
∑
n
=
1
∞
1
n
(
n
+
1
)
\sum_{n=1}^{\infty} \frac{1}{n(n+1)}
∑
n
=
1
∞
n
(
n
+
1
)
1
correct to within 0.01 using the integral test. b) Compute the limit of the series exactly and compare. Hint: The sum telescopes.
Related theory
Improper Integrals Convergence
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