Let \{a_n \}_{n \geq 1} be a sequence of real numbers such that a1+5m=2 , a2+5m=3 , a3+5m=4 , a4+5m=5, a5+5m=6 , m=0,1,2, … . Then
\limsup_{n \rightarrow \infty} a_n + \liminf_{n \rightarrow \infty} a_n equals ____________________________ .
It is evident that an is defined for all values of n=1,2,3,…. . And so
sup \quad a_n = 6 ,\quad inf \quad a_n = 2 \\
So, \limsup_{n \rightarrow \infty} a_n + \liminf_{n \rightarrow \infty} a_n = 8