Find the Sum of the Series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( 5 n - 1 ) ( 5 n + 1 ) }$

question 144

Multiple Choice

Find the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( 5 n - 1 ) ( 5 n + 1 ) }$ .

• A) \(\frac { 1 } { 5 }\)
• B) \(\frac { 1 } { 6 }\)
• C) \(\frac { 1 } { 2 }\)
• D) \(\frac { 1 } { 10 }\)
• E)1
• F) \(\frac { 3 } { 4 }\)
• G) \(\frac { 3 } { 2 }\)
• H)Divergent

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Definitions:

Notochord

A flexible rod-shaped body found in the embryonic stage of all chordates that provides skeletal support.

Longitudinal

Pertaining to research or studies that follow the same subjects over a period of time to observe changes.

Flexible Rod

A structural element that is capable of bending or flexing under load while maintaining its integrity.

Nervous Systems

The nervous system is the complex network of nerve tissue that controls activities within the body by transmitting electrical and chemical signals between different body parts.