Prove that sequence (-1)^{n} is not convergent .

Kyran Hudson

Kyran Hudson

Answered question

2021-03-02

Prove that sequence (1)n is not convergent .

Answer & Explanation

Szeteib

Szeteib

Skilled2021-03-03Added 102 answers

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.

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