Using the definition of a convergent sequence, prove \lim_{n\to\infty}\frac{1}{n^2}=0 Don't use any

Falak Kinney

Falak Kinney

Answered question

2021-08-18

Using the definition of a convergent sequence, prove
limn1n2=0
Don't use any theorems about convergent sequences

Answer & Explanation

Szeteib

Szeteib

Skilled2021-08-19Added 102 answers

Let ϵ be any positive number
We need to show that |1n20|<ϵ
Now take NϵN, 1ϵ<N. 1N<ϵ
n>N(i.e.1n<1N). 1ϵ<N
and |1n20|=|1n2|=1n2<1N<ϵ; (1n2 is always positive)
Hence |1n20|<ϵ
limn1n2=0

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-23Added 2605 answers

Answer is given below (on video)

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