tag:blogger.com,1999:blog-3550204829234352390.post4465276089835483194..comments2024-03-27T09:13:48.546+08:00Comments on 研發養成所 ( Bridan's Blog - 4rdp, For R&D Person ): 訓練數學感 70 ─ 格子點Bridanhttp://www.blogger.com/profile/17055047757114667099noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3550204829234352390.post-9396264784059456782015-09-04T19:50:35.777+08:002015-09-04T19:50:35.777+08:00You are right.
a1=0=1*0
a2=2=2*1
a3=6=3*2
a4=12=4*...You are right.<br />a1=0=1*0<br />a2=2=2*1<br />a3=6=3*2<br />a4=12=4*3<br />:<br /><br />So actually, an = n(n-1)Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-39491566055693190072015-09-04T19:50:02.069+08:002015-09-04T19:50:02.069+08:00You are right.
a1=0=1*0
a2=2=2*1
a3=6=3*2
a4=12=4*...You are right.<br />a1=0=1*0<br />a2=2=2*1<br />a3=6=3*2<br />a4=12=4*3<br />:<br /><br />So actually, an = n(n-1)Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-6857354081585321772015-09-03T23:45:12.470+08:002015-09-03T23:45:12.470+08:00First, an must be positive integer.
by putting n=1...First, an must be positive integer.<br />by putting n=1,n=2 ,n=3 into an = (n+1)(2n+1)/2 - n -(2n+1) = (2n^2 - 3n -1)/2,<br />we may get a negative number or fraction.<br /><br />小文noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-10293634101098945582015-09-02T09:29:02.513+08:002015-09-02T09:29:02.513+08:00Hi 小文,
Regarding the an, it isn't equal to (n...Hi 小文,<br /><br />Regarding the an, it isn't equal to (n+1)^2.<br /><br />It should be<br />an = (n+1)(2n+1)/2 - n -(2n+1) = (2n^2 - 3n -1)/2<br /><br />The final result is equal to 1.Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-39996888347769954772015-09-02T00:15:44.755+08:002015-09-02T00:15:44.755+08:001 ?
First, we have to find the relation between a...1 ? <br />First, we have to find the relation between an and n. <br />Second, find the limit.<br /><br />Result : an = (n+1) ^2 <br />an / n^2 = 1 + 2*n^-1 + n^-2<br />as n tends to infinity, n^-1 and n^-2 tend to 0.<br />Thus, the final result should be 1.小文noreply@blogger.com