# Help find Lim Sup and Lim Inf of the following sequences:

I'll be honest just looking for confirmation of my answers. I have been given the sequences $$S_n= \pi+(-1)^n$$, $$A_n=\pi+(-0.5)^n$$, $$B_n=\pi+(-2)^n$$.

I am asked to find Limsup and LimInf for each sequence and I have tried by simply observing that there are only 2 subsequences for each sequence those being $$S_{2n}$$ and $$S_{2n-1}$$ which when finding the limits I find the results:

$$LimSup(S_n)=\pi+1, LimInf(S_n)=\pi-1$$

$$LimSup(A_n)=LimInf(A_n)=\pi$$

$$LimSup(B_n)=+∞, LimInf(B_n)=-\infty$$

Am I doing this the correct way for sequences that oscillate between positive and negative?

• Looks right to me. Maybe show more prooflike details,,, – coffeemath Oct 9 '18 at 2:01