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Question Number 59089 by Tawa1 last updated on 04/May/19

Answered by arcana last updated on 08/Jun/19

let m,n≥1,m>n x_m −x_n =x_m −x_(m−1) +x_(m+1) −x_(m−2) +...+x_(n+1) −x_n ∣x_m −x_n ∣≤∣x_m −x_(m−1) ∣+∣x_(m−1) −x_(m−2) ∣+...+∣x_(n+1) −x_n ∣ ≤cσ^(m−1) +cσ^(m−2) +...+cσ^(n+1) +cσ^n ≤c+c+...+c≤c(m−1−n)

letm,n⩾1,m>nxm−xn=xm−xm−1+xm+1−xm−2+...+xn+1−xn∣xm−xn∣⩽∣xm−xm−1∣+∣xm−1−xm−2∣+...+∣xn+1−xn∣⩽cσm−1+cσm−2+...+cσn+1+cσn⩽c+c+...+c⩽c(m−1−n)

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