Which of the Following Series Converges?
1) $\sum _ { n = 1 } ^ { \infty } \sin \left( \frac { 1 } { n ^ { 2 } } \right)$

question 173

Multiple Choice

Which of the following series converges?
1) $\sum _ { n = 1 } ^ { \infty } \sin \left( \frac { 1 } { n ^ { 2 } } \right)$
2) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \sqrt [ 3 ] { n } }$
3) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 n + 1 } { 2 n + 1 } \right) ^ { n }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

---

Definitions:

Trade Deficit

A situation in which a country's imports of goods and services exceed its exports, leading to a negative balance of trade.

Federal Government

The national government of a country, which is responsible for governing the nation as a whole and enacting laws applicable across all states or provinces.

Securities or Assets

Financial instruments that hold value and can be traded, such as stocks, bonds, or real estate.

Currency Interventions

Actions taken by a country's central bank or government to influence the value of its currency in the foreign exchange market.