The limit of the infinite series is [tex]\frac{3}{4}[/tex]
Definition of limit :
- A function f(x) limit exist at x = a if,
[tex]\lim_{x \to a+} f(x)= \lim_{x \to a-} f(x)=f(a)[/tex]
- The limit of a series is the value the series when n approaching n → ∞ .
- Given function is,
[tex]\sum_{n=1}^{\infty} \frac{3n^{5} }{4n^{5}+1 }[/tex]
The value of limit of a series is ,
[tex]\lim_{n \to \infty} \frac{3n^{5} }{4n^{5}+1 }=\frac{3n^{5} }{n^{5}(4+\frac{1}{n^{5} } ) }\\\\ \lim_{n \to \infty} \frac{3 }{(4+\frac{1}{n^{5} } ) }=\frac{3}{4}[/tex]
The limit of the infinite series is [tex]\frac{3}{4}[/tex]
Learn more about the limit of the function here:
https://brainly.com/question/1444047
