A Statement $$\mathrm { S } _ { \mathrm { n } }$$

question 223

Essay

A statement
$$\mathrm { S } _ { \mathrm { n } }$$ about the positive integers is given. Write statements
$\mathrm { S } _ { 1 } , \mathrm {~S} _ { 2 }$ and S
$\mathrm { S } _ { 3 }$ , and show that each of these
statements is true.
- $$S _ { n } : 2 \text { is a factor of } n ^ { 2 } + 9 n$$

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Definitions:

American System

An economic plan advocated by Henry Clay in the early 19th century, emphasizing support for a national bank, high tariffs, and internal improvements to foster national economic growth.

Panic of 1819

The first major financial crisis in the United States, which occurred due to a sudden collapse of the economy, leading to bank failures and unemployment.

European Market

The combined economies of European countries, often referring to the single market in the context of the European Union.