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:

Manic-depressive Disorder

An old term for bipolar disorder, a mental health condition characterized by extreme mood swings.

Chemical Imbalance

A hypothetical concept suggesting that mental health conditions arise from an imbalance of chemicals in the brain.

Traditional Classification

A system of categorization based on longstanding and conventional criteria or principles.

Mental Disorders

A broad range of conditions affecting mental health, characterized by alterations in thinking, mood, or behavior associated with distress or impaired functioning.