Determine whether the sequence an = (-1)n is convergent or divergent. | Mathematics I 2081

Mathematics I20815 marksNumerical: sequence convergenceInfinite sequence and series

Determine whether the sequence $a_n = (-1)^n$ is convergent or divergent. [5]

Given: - Sequence: $an = (-1)^n$ No other numeric data required. This is a proof-based analysis problem. --- $a1 = -1,\quad a2 = +1,\quad a3 = -1,\quad a4 = +1,\quad \dots$ The sequence oscillates permanently between $+1$ and $-1$ . A sequence $\{an\}$ converges to a limit $L$ if for every

Given: - Sequence: $an = (-1)^n$ No other numeric data required. This is a proof-based analysis problem. --- $$a1 = -1,\quad a2 = +1,\quad a3 = -1,\quad a4 = +1,\quad \dots$$ The sequence oscillates permanently between $+1$ and $-1$. A sequence ${an}$ converges to a limit $L$ if for every

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