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?Determine whether the series is convergent or
Chapter 9, Problem 14(choose chapter or problem)
QUESTION:
Determine whether the series is convergent or divergent.
\(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{13}+\cdots\)
Questions & Answers
QUESTION:
Determine whether the series is convergent or divergent.
\(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{13}+\cdots\)
ANSWER:Step 1 of 3
Integral test: let f be a non-negative decreasing function on \((1, \infty)\). Then the series \(\sum_{n=1}^{\infty} f(x)\) and the improper integral \(\int_{1}^{\infty} f(x) d x\) converge or diverge together on \((1, \infty)\) if \(\int_{1}^{\infty} f(x) d x=\text { finite }\) then the series will be convergent otherwise divergent.