If this sequence converged, then every subsequence will converge to the same limit. However notice that this sequence goes as follows:

\(1,−1,1,−1,1,−1,...\) As \(n=0,1,2,3,4,5,...\)

Therefore, notice that for even nn values, we have the subsequence 1,1,1,1,1,...1

which obviously converges to 1, while for odd nn values, we have the subsequence

−1,−1,−1,−1,..., which obviously converges to −1.

herefore, since both subsequences converge to different values (1 and −1), we have that this sequence does not converge.

\(1,−1,1,−1,1,−1,...\) As \(n=0,1,2,3,4,5,...\)

Therefore, notice that for even nn values, we have the subsequence 1,1,1,1,1,...1

which obviously converges to 1, while for odd nn values, we have the subsequence

−1,−1,−1,−1,..., which obviously converges to −1.

herefore, since both subsequences converge to different values (1 and −1), we have that this sequence does not converge.