Prove the Following Statement by Mathematical Induction $3+7+11+\cdots+(4 n-1)=n(2 n+1)$

question 24

Essay

Prove the following statement by mathematical induction: $3+7+11+\cdots+(4 n-1)=n(2 n+1)$

---

Definitions:

Dominance Hierarchies

Social ranking systems within animal groups, where individuals are ranked in terms of access to resources.

Primatologists

Scientists who study primates, including monkeys, apes, and humans, focusing on their behavior, biology, and evolution, and their interactions with environments and societies.

Nonhuman Primates

Primates that are not human beings, including monkeys, apes, and lemurs, often studied to gain insights into human evolution and behavior.

Teams

Groups of individuals working together towards a common goal, characterized by shared responsibilities and collaborative effort.