Answer on Real Analysis Question for Matthew Lind
We should prove that
lim 1/a_n = 0.
Fix any epsilon>0 and take A = 1/epsilon.
Since lim a_n = - infinity, there exists N such that forall n>N we have that a_n < -A
|a_n| > A
|1/a_n| < 1/A =epsilon.
Thus for all n>N
This means that lim 1/a_n = 0.
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