What limit of |an| / |an+1| as n: infinity of given attached an

Mathematics
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Dec 14th, 2014

an  = n1/n

an+1 = (n+1)1/n+1

an+1 /an =(n+1)1/n+1/ n1/n

log an+1 /an = (1/(n+1)) ln (n+1)/(1/n) ln(n)= n/(n+1) ln (1+1/n)  -> 0 as n-> ∞

an+1 /an -> 1

an/an+1 -> 1


an =  1/(n(n+i)(n+2)

an+1 =  1/(n+1)(n+1+i)(n+3)

an+1 /an  = n(n+i)(n+2)/(n+1)(n+1+i)(n+3) -> 1 as n- >  ∞

an/an+1 -> 1


Dec 14th, 2014

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