Find the limit infimum and the limit supremum of each of the following sequences a) xn 3 ( 1)n b) xn cos n 2) c) xn ( l)n 1 ( )n n d) xn 1 n2 (2n 5) e) xn yn n, where yn is any bounded sequence f) xn n(1 ( 1)n) n 1(( 1)n 1) g) xn (n3 n2 n l) (n2 2n 5) ...

a Since 31 n 2 when n is even and 4 when n is odd lim sup n x n 4 ...

Find the limit infimum and the limit supremum of each of the following sequences. a) xn =

Question:

Find the limit infimum and the limit supremum of each of the following sequences.
a) xn = 3-(-1)n
b) xn = cos {nπ/2)
c) xn = (-l)n+1 + (-!)n/n
d) xn = √1 + n2/(2n - 5)
e) xn = yn/n, where {yn} is any bounded sequence
f) xn = n(1 + (-1)n) + n-1((-1)n - 1)
g) xn = (n3 + n2 - n + l)/(n2 + 2n + 5)