Question Number 148519 by learner001 last updated on 28/Jul/21

a_n =(n/(n+1)) let ε>0 be given, ∣a_m −a_n ∣=∣(m/(m+1))−(n/(n+1))∣=∣((m−n)/((m+1)(n+1)))∣=((m−n)/((m+1)(n+1))) provided m>n, ((m−n)/((m+1)(n+1)))<((m+1)/((m+1)(n+1)))=(1/(n+1))<ε. if N>((1−ε)/ε) then ∣a_m −a_n ∣<ε ∀ n,m≥N

Commented bylearner001 last updated on 28/Jul/21

can someone check if the proof I made is correct? I was trying to show that the sequence is Cauchy.