[分析] limit at infinity

[laba5566 (最愛56家族 啾咪)]

let f : N -> R

if  lim  f(n+1)- f(n) = L
    n->∞

show that   lim  f(n)/n equals L
            n->∞

是wade裡的習題 感覺不難但是卡住了

希望版上高手能解救一下 Orz

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→ laba5566    :謝謝 不過我沒有連續這個條件 還可以作嗎
推 GaussQQ     :Let s_n=f(n)-f(n-1) then the question change to
→ GaussQQ     :If s_n->L as n goes to infinite then sum(s_n)/n
→ GaussQQ     :->L as n goes to infinite.
→ GaussQQ     :This is a standard question in the content of
→ GaussQQ     :sequence.
→ sato186     :樓上好解!!
→ laba5566    :感謝上面幾位版友！！