a) an= cos(n(pi)) b) an= sin^-1( )
c) an= e^(4-n^2)
a)
$\displaystyle cos((2k)pi)=1$
$\displaystyle cos((2k+1)\pi)=-1$
You tell me, could it converge to anything?
b)what is $\displaystyle lim_{n\rightarrow \infty}\frac{2-3n+n^2}{5+2n^2}$?
multiply by $\displaystyle \frac{1/n^2}{1/n^2}$ and see what happens. Hint: you should get 1/2.
Recall: $\displaystyle sin(\pi/6)=1/2$
c)what is what is $\displaystyle lim_{n\rightarrow \infty} 4-n^2 $?
Hint: $\displaystyle e^{-x}=\frac{1}{e^x}$