Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \left( \tan ^ { - 1 } ( n + 1 ) - \tan ^ { - 1 } n \right)$$

question 31

Multiple Choice

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

• A) converges; \(\frac { \pi } { 2 }\)
• B) converges; \(\pi\)
• C) diverges
• D) converges; \(- \frac { \pi } { 2 }\)

Understand the concept of convex preferences and how they relate to commodity bundles and consumer preferences.

Comprehend the principles of transitivity in consumer preferences and its implications on choice.

Grasp the calculation and significance of marginal rates of substitution in indifference curves.

Analyze how different pricing affects consumer choices and the marginal rate of substitution between goods.

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