Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \frac { 2 } { n ( n + 1 ) ( n + 2 ) }$$

question 150

Multiple Choice

Determine if the series converges or diverges. If the series converges, find its sum.
- $$\sum _ { n = 1 } ^ { \infty } \frac { 2 } { n ( n + 1 ) ( n + 2 ) }$$

• A) converges; \(\frac { 4 } { 3 }\)
• B) converges; \(\frac { 1 } { 2 }\)
• C) converges; \(\frac { 3 } { 2 }\)
• D) diverges

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Definitions:

Generalization

The tendency, once a response has been conditioned, for stimuli similar to the conditioned stimulus to elicit similar responses. In operant conditioning, generalization occurs when responses learned in one situation occur in other, similar situations.

Discrimination

The unfair or prejudicial treatment of different categories of people, often based on race, age, sex, or disability.

Classical Conditioning

An acquisition method where two stimuli are frequently paired; the response, at first prompted by the second stimulus, is later prompted by the first stimulus in isolation.

Reinforcer

Any stimulus that, when presented after a behavior, increases the likelihood of that behavior occurring again in the future.