Use Mathematical Induction to Prove the Following Inequality for All $n \geq 2$

question 12

Essay

Use mathematical induction to prove the following inequality for all $n \geq 2$ .
$$\frac { 1 } { \sqrt { 23 } } + \frac { 1 } { \sqrt { 46 } } + \frac { 1 } { \sqrt { 69 } } + \ldots + \frac { 1 } { \sqrt { 23 n } } > \frac { \sqrt { n } } { \sqrt { 23 } }$$

---

Definitions:

Structured Information

Organized data that adheres to a predefined format, making it easily searchable and manageable by computer systems.

Unstructured Information

Data or information that lacks a predefined model or organization, making it difficult to process and analyze using traditional databases or methods.

Volume

In business and finance, it refers to the quantity of goods or services traded during a given time period. In the context of stock markets, it indicates the number of shares traded.

Velocity

The speed at which something moves in a specific direction, often used in the context of data to refer to the rate of data transfer or processing.