I'm wondering about the motivation for proving the limit. <mstyle displaystyle="true" scriptleve

Waylon Ruiz 2022-05-26 Answered
I'm wondering about the motivation for proving the limit.
lim x 1 x n = 1
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Answers (1)

xxsailojaixxv5
Answered 2022-05-27 Author has 10 answers
Lets go to the definition of the limit.
ϵ > 0 , δ > 0 : | x 1 | < δ | x n 1 | < ϵ
The "trick" here will be very similar to the one above, but it might look more natural here.
Multiplying by "1."
| x n 1 1 1 + x n + x n 2 + + x n n 1 1 + x n + x n 2 + + x n n 1 | = | x 1 1 + x n + x n 2 + + x n n 1 |
let δ 1 then x > 0 and 1 + x n + x n 2 + + x n n 1 > 1
| x n 1 | < | x 1 | < δ
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