Use Mathematical Induction to Prove the Following for Every Positive $n$

question 48

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }$

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Definitions:

Gender Typing

The process by which individuals are taught and learn the behaviors, interests, and abilities considered appropriate for their gender in their culture.

Primary Sex Characteristics

are the biological and physical traits directly involved in reproduction, such as the ovaries in females and testes in males.

Secondary Sex Characteristics

Physical features that appear during puberty which are not directly involved in reproduction, such as breast development in females and beard growth in males.

Gender Schemas

Cognitive structures that organize beliefs and expectations about gender, guiding how individuals process gender-relevant information.