Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to \( \infty \), and infinity if it diverges to \( -\infty \). Otherwise, enter diverges. \[ \int_{2}^{\infty} \frac{d x}{(8 x-2)^{6}}= \] Does the series \( \sum_{n=2}^{\infty} \frac{1}{(8 n-2)^{6}} \) converge or diverge??
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We can approach this by considering a definite integral with a variable upper limit and then taking the limit as that upper limit approaches infinity. Show more…
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