Which of the Three Series Below Converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { \sqrt [ 5 ] { n ^ { 4 } } } + \frac { 2 } { n ^ { 3 } } \right)$

question 258

Multiple Choice

Which of the three series below converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { \sqrt [ 5 ] { n ^ { 4 } } } + \frac { 2 } { n ^ { 3 } } \right)$
2) $\sum _ { n = 1 } ^ { \infty } \frac { \ln n } { n ^ { 2 } }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { \sin ( 1 / n ) } { n }$

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

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Definitions:

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good, reflecting the goods' sensitivity to price changes.

New York

A state in the northeastern United States, known for its significant cultural, financial, and political influence, as well as being home to New York City, one of the largest and most iconic cities globally.

Florida

A southeastern U.S. state, known for its beaches, theme parks, and warm climate.

Midpoint Formula

A method used in economics to calculate the elasticity of a demand or supply curve, representing the percentage change in quantity demanded or supplied relative to a percentage change in price.