Find the Values of P for Which the Series Is $\sum _ { n = 1 } ^ { \infty } 4 n \left( 1 + n ^ { 2 } \right) ^ { p }$

question 32

Short Answer

Find the values of p for which the series is convergent. $\sum _ { n = 1 } ^ { \infty } 4 n \left( 1 + n ^ { 2 } \right) ^ { p }$

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Definitions:

Tariff

A tax imposed by a government on goods imported from another country, intended to increase the price of foreign goods and protect domestic industries.

Oranges

A type of citrus fruit known for its juicy segments and rich source of Vitamin C.

Domestic Production

The total value of all goods and services produced within a country's borders in a given time period.

Imported Shoes

Footwear that is brought into a country from abroad for sale, typically subject to tariffs, quotas, or other trade regulations.