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Let a_n=(1/n).we claim that (a_n)_n=1(n goes to infinite) converges to 0.now for ε >0 let n_0=[1/ε]+1.
So we have n_0>(1/ ε).heance for n>n_0 we have 0<(1/n)<(1/n_0)< ε.
sir Please describe it.
Let me rephrase it so it makes more sense.
Let a_n = (1/n).
We claim that if (a_n)•n = 1 for all n, then as n goes to infinity, a_n converges to 0.
I'm not sure this next part sound right:
Now for some ε > 0, let n_0 = [1/ε] + 1, we have n_0>(1/ ε).
What I think it should sound like is,
"For any ε > 0, n can be chosen large enough so that for every a_m where m>=n, a_m < ε."
Now for the last line, "Hence for n>n_0 we have 0<(1/n)<(1/n_0)< ε,"
it is equivalant to saying that for n>n_0, 0 < a_n < a_n0 < ε.
This sounds like a proof that the series 1/n converes to 0 as n goes to infinity.
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Scott A Wilson
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