Re: [積分] 定積分
※ 引述《youyouyou (第3年高3生活)》之銘言：
: ※ 引述《terry1122 (我會一直守候著你)》之銘言：
: : lim 1 n n n
: : { --- + ------- + ------- +......+ --------- }
: : n->∞ n (n+1)^2 (n+2)^2 (2n+1)^2
: n+1 1 1 1 1 -1 π
: lim Σ ( --- ) * ( ------------ ) = ∫ --------dx = tan 1 = ---
: n->∞ i=0 n [1+(i/n)^2 0 (1+x^2) 4
^^^^^^^^^^^^
當i=1時， 1 1 n
( --- ) * ( ------------ ) (上下同乘n^2) = ---------------
n 1+ 1/n^2 n^2+1
n
與原式 -------- 不合
(n+1)^2
==========================================================================
lim 1 n n n
{ --- + ------- + ------- +......+ --------- }
n->∞ n (n+1)^2 (n+2)^2 (2n+1)^2
lim n n n n
= { ------- + ------- + ------- +......+ --------- }
n->∞ (n+0)^2 (n+1)^2 (n+2)^2 (n+ n+1)^2
lim n+1 n
= Σ { ------- } 上下同除n^2
n->∞ i=0 (n+i)^2
lim n+1 1 1
= Σ { ------- * ---}
n->∞ i=0 (1+i/n)^2 n
1 1
= ∫ ------- * dx
0 (1+x)^2
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.138.216.105
推
140.115.213.118 03/25, , 1F
140.115.213.118 03/25, 1F
→
140.115.213.118 03/25, , 2F
140.115.213.118 03/25, 2F
推
220.138.216.105 03/25, , 3F
220.138.216.105 03/25, 3F
推
220.137.67.113 03/25, , 4F
220.137.67.113 03/25, 4F
推
140.115.213.118 03/25, , 5F
140.115.213.118 03/25, 5F
→
140.115.213.118 03/25, , 6F
140.115.213.118 03/25, 6F
討論串 (同標題文章)