Final answer:
The statement is false; the value of an improper integral used in the integral test does not match the sum of a telescoping series. The integral test is for convergence, while the actual sum of a telescoping series comes from remaining terms after cancellation.
Step-by-step explanation:
False. The value of the improper integral from the integral test does not necessarily match the sum of a telescoping series. The integral test is a method used to determine the convergence or divergence of an infinite series by comparing it to an improper integral. If the integral converges, then the series also converges, and if the integral diverges, the series does the same. However, the actual value of the improper integral is not used to find the sum of the series; it is only used to determine convergence. In contrast, a telescoping series is a special type of series where most terms cancel out with other terms in the series, leaving only a few terms for finding the sum. The actual values that remain are used to find the sum of the series, which is unrelated to the value of the corresponding integral.