Use Mathematical Induction to Prove That $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$

question 34

Essay

Use mathematical induction to prove that $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$

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Definitions:

Insect And Fish Dyes

Natural dyes derived from insects, such as cochineal for red color, or fish, used historically for textile dyeing and in art materials.

Printmakers

Artists specialized in creating artworks through the process of printmaking, including techniques like etching, engraving, lithography, and screen printing.

Ando Hiroshige

A prominent Japanese ukiyo-e artist of the Edo period known for his landscapes, especially the series "The Fifty-three Stations of the Tokaido."

Katsushika Hokusai

A renowned Japanese artist and printmaker of the Edo period, best known for his woodblock print series "Thirty-Six Views of Mount Fuji."