Find The $n ^ { \text {th } }$ Partial Sum $S _ { n }$

question 19

Short Answer

Find the $n ^ { \text {th } }$ partial sum $S _ { n }$ of the telescoping series, and use it to determine whether the series converges or diverges. If it converges, find its sum. $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { n + 10 } - \frac { 1 } { n + 8 } \right)$

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Definitions:

Retinal Disparity

Retinal disparity refers to the slight difference in the visual images that reach each eye, which is then processed by the brain to perceive depth, forming the basis of stereopsis.

Different Images

Visual representations that are not identical, showcasing variations in appearance, perspective, or content.

Necker Cube

An optical illusion of a wireframe cube that can be perceived from different perspectives.

Top-Down Processing

A cognitive process that initiates with our thoughts, which flow down to lower-level functions such as the senses; relying heavily on previous experience and expectations in perception.