Use the Integral Test to Determine Whether the Infinite Series $\sum _ { k = 2 } ^ { \infty } \frac { 2 } { 2 k + 1 }$

question 10

Short Answer

Use the integral test to determine whether the infinite series $\sum _ { k = 2 } ^ { \infty } \frac { 2 } { 2 k + 1 }$ is convergent or divergent. Then use the comparison test to determine whether the infinite series $\sum _ { \mathrm { k } = 1 } ^ { \infty } \frac { 4 } { \mathrm { k } + 1 }$ is convergent or divergent.
Enter just two words which answer the two questions above in order (separated by a comma) where each word is either "convergent" or "divergent".

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Definitions:

Population Average

The sum of all values in a population divided by the number of values in that population, also known as the mean.

Standard Error

The standard deviation of the sampling distribution of a statistic, often used to estimate the accuracy of a sample mean.

Population Standard Deviation

A measure of the dispersion or variability within a full population, indicating how much individual points differ from the population mean.

Sample Size

The number of individual observations or data points collected and included in a sample from a population for analysis.