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

question 11

Essay

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

---

Definitions:

Biochemical Changes

Alterations in the chemical processes and substances within living organisms, often referring to changes that affect mood, behavior, and cognition.

Brain Waves

Patterns of electrical activity in the brain, indicative of different states of consciousness, such as wakefulness or sleep.

Positron-Emission Tomography

A diagnostic imaging technique that uses radioactive substances to visualize and measure changes in metabolic processes.

Biochemical Activity

The chemical processes and reactions that occur within living organisms.