Determine Whether the Sequence Defined By $a _ { n } = \left( 1 + \frac { 5 } { n } \right) ^ { 1 / n }$

question 127

Short Answer

Determine whether the sequence defined by $a _ { n } = \left( 1 + \frac { 5 } { n } \right) ^ { 1 / n }$ converges or diverges. If it converges, find its limit.

---

Definitions:

I Proposition

In traditional logic, an "I proposition" is a type of categorical proposition that affirms some, but not all, members of the subject class are members of the predicate class, often structured as "Some S are P."

Explicit Quantifiers

Symbols or phrases in logic that explicitly specify the quantity of subjects to which a statement applies.

Universal

A term referring to concepts, properties, or statements that apply universally, without exceptions.

Particular

In philosophy, an individual object as opposed to a universal quality; distinguished from general or universal by being specific or detailed.