- #1
will_lansing
- 19
- 0
Homework Statement
Find the limit of the sequence whose terms are given by [tex]a_{n}[/tex]=[tex]n^{2}[/tex](1-cos[tex]\frac{4.2}{n}[/tex])
Homework Equations
The Attempt at a Solution
I now that [tex]n^{2}[/tex] goes to infinity so have to use l'hospital rule because you will have infinity*0 which is an indeterminate form, so rewrote as
[tex]a_{n}[/tex]=[tex]\frac{(1-cos\frac{4.2}{n})}{\frac{1}{n^{2}}}[/tex]
[tex]lim_{n\rightarrow\infty}[/tex] [tex]\frac{(1-cos\frac{4.2}{n})}{\frac{1}{n^{2}}}[/tex] [tex]\frac{}{}[/tex]
= [tex]lim_{n\rightarrow\infty}\frac{ [/tex] {[tex]\frac{-4.2sin\frac{4.2}{n}}{n^{2}}[/tex]}/{[tex]\frac{-2}{n^{3}}[/tex]}
won't the limit still be 0 i really don't understand any of this can anyone please help