# Warm Yourself With An MCQ

# Understand the problem

##### Source of the problem

##### Topic

##### Difficulty Level

##### Suggested Book

# Start with hints

Now the limit points of this set are those points which the set does not attain.So, they might be the sup and inf which are not attained by this set. Basically sup(\(a_n\))= max{ limit points, \(a_n\) | n \(\in\) \(\mathbb{N}\)} Limit points are \(2,1\) and \(a_1= 2+1=3, a_3= 2- \frac{1}{3} ; a_5= 2+\frac{1}{5} \) \(a_0= 1+1=2 , a_2= 1+ \frac{1}{4} , a_3= 1+\frac{1}{8} \) Now you can calculate the supremum?

inf \(a_n\)= min {2,1,2 -\(\frac{1}{3}\)}=1 So, option A is correct. Now there is another question regarding lim sup and lim inf. We can observe that we have mainly \(3\) subsequences , corresponding to \( n\) is even; \(n=2k\) \(n\)= \(4k+1\) \(n=4k+3\)

Can you calculate the corresponding subsequences and their limits?

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