Re: [積分] riemann sum
※ 引述《metastable (亞穩)》之銘言：
: pn qn
: lim (Σ 1/k - Σ 1/k)
: n→∞ k=1 k=1
: pn
: = lim Σ 1/k (r is euler constant)
: n→∞ qn+1
: (1+ 1/2 +.....+1/n) r + ln(n) L
: lim --------------------- = lim -------------- = 0
: n n
: (1+ 1/2 + ....+1/2n) r + ln(2n) L
: lim --------------------- = lim -------------- = 0
: n n
: (1+ 1/2 +.....+1/n) r + ln(n) L
: lim --------------------- = lim -------------- = 1
: ln(n) ln(n)
: 我看不懂上面三行是怎來的 請幫我解釋
Euler's constant is defined by
Let H = 1 + (1/2) + (1/3) + ... + (1/n)
γ = lim [ H - ln(n) ]
n→∞
----
( 1 + ... + 1/n ) H - ln(n) + ln(n)
lim ------------------- = lim -------------------
n→∞ n n→∞ n
γ + ln(n)
= lim -----------
n→∞ n
L' 1
= lim ----- = 0
n→∞ n
其餘同理
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