a_{n } = n^{1/n}

a_{n+1} = (n+1)^{1/n+1}

a_{n+1} /a_{n }=(n+1)^{1/n+1}/ n^{1/n}

log a_{n+1} /a_{n }= (1/(n+1)) ln (n+1)/(1/n) ln(n)= n/(n+1) ln (1+1/n) -> 0 as n-> ∞

a_{n+1} /a_{n} -> 1

a_{n}/a_{n+1} -> 1

a_{n} = 1/(n(n+i)(n+2)

a_{n+1} = 1/(n+1)(n+1+i)(n+3)

a_{n+1} /a_{n} = n(n+i)(n+2)/(n+1)(n+1+i)(n+3) -> 1 as n- > ∞

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