Question

Let an = n
n + 1
. Find a number M such that:
(a) |an − 1| ≤ 0.001 for n ≥ M.
(b) |an − 1| ≤ 0.00001 for n ≥ M.
Then use the limit definition to prove that lim
n→∞
an = 1.

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