(11) Which of the following statements imply that {an} converges to a? (a) For every integer m > 0, there is an integer N > 0 such that |an – a| N. (b) For each 0 0 such that |an- a| N. (c) For each 0 0 such that |an- a| N. (d) For each N > 0, there is ɛ > 0 such that |an – a| N + ɛ . \text { (e) For each } \varepsilon>0 \text { , there is an integer } N>0 \text { such that }\left|a_{n}-\alpha\right| N^{2} \text { . } (f) For each ɛ > 0, there is an integer N > 0 such that an – a 0, there is an integer N > 0 such that |an – a| < ɛ when n = N + 2k for all positive integer k.

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11 which of the following statements imply that an converges to a a fo

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(11) Which of the following statements imply that {an} converges to a? (a) For every integer m > 0, there is an integer N > 0 such that |an – a| < 1/m when n> N. (b) For each 0 < ɛ < 1, there is an integer N > 0 such that |an- a| < 3ɛ when n > N. (c) For each 0 < ɛ < 1, there is an integer N> 0 such that |an- a| < 1/ɛ