Question

7. Show that the function determined by the terms of the given series satisfies the hypotheses of the Integral Test, and then use the Integral Test to determine whether the series sum converges or diverges $\sum_{k=1}^{\infty} \frac{1}{k^2 - 1}$ (a) Make a plot of: $f(x) = \frac{1}{x^2 - 1}$ (b) Is f(x) always positive and decreasing from 1 <= x < +inf ? (yes or no) (c) Perform the integral test. Does the series converge, diverge, or inconclusive? (d) Perform the p-test. Does the series converge, diverge, or inclusive. (e) If your answers to (c) and (d) are difference, how do you resolve the difference?

          7.
Show that the function determined by the terms of the given series
satisfies the hypotheses of the Integral Test, and then use the Integral Test to
determine whether the series sum converges or diverges
$\sum_{k=1}^{\infty} \frac{1}{k^2 - 1}$
(a) Make a plot of: $f(x) = \frac{1}{x^2 - 1}$
(b) Is f(x) always positive and decreasing from 1 <= x < +inf ? (yes or no)
(c) Perform the integral test. Does the series converge, diverge, or inconclusive?
(d) Perform the p-test. Does the series converge, diverge, or inclusive.
(e) If your answers to (c) and (d) are difference, how do you resolve the
difference?

7.
Show that the function determined by the terms of the given series
satisfies the hypotheses of the Integral Test, and then use the Integral Test to
determine whether the series sum converges or diverges
∑k=1^∞(1)/(k^2 - 1)
(a) Make a plot of: f(x) = (1)/(x^2 - 1)
(b) Is f(x) always positive and decreasing from 1 <= x < +inf ? (yes or no)
(c) Perform the integral test. Does the series converge, diverge, or inconclusive?
(d) Perform the p-test. Does the series converge, diverge, or inclusive.
(e) If your answers to (c) and (d) are difference, how do you resolve the
difference?

Added by Courtney S.

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