Prove,by mathematical induction,that 1x2+2x3+3x4+...+n(n+1)=(1/3)n(n+1)(n+2) for all positive integers n.
Hence evaluate 1x3+2x4+3x5+...+50x52.
有冇人識計唷=.=
最好詳細步驟+說明= =
因為我唔多明點計-..-
感謝><
中四A-MATH題=.=
2008-10-31 2:43 am
回答 (3)
2008-10-31 3:11 am
2008-10-31 3:52 am
您信我用這方法可以幫助您解決身體問題, 碧咸球隊都是用它.
你係咪想型d, fit d又健康d?
我個女13歲, 都是用這方法, 一個月減10磅, 三個月減20磅.
改善鼻敏感, 流鼻血, 靚咗, FIT咗, 讀書仲好咗, 仲拿第一添.
我做文職, 133磅, 160CM , 用咗簡單又健康既方法!
我用左4個月減左20磅, 改善頭痛,胃痛, 暈車浪,植物曲脹, 越來越fit!面色仲好過以前!
網站可以增肥, 減肥, 改善身形, 健康, 體重控制,
美容護膚, http://www.healthcometrue.com/life
[[有營養顧問免費跟進^^ ]]
TEL: 93227176 阿紅
你係咪想型d, fit d又健康d?
我個女13歲, 都是用這方法, 一個月減10磅, 三個月減20磅.
改善鼻敏感, 流鼻血, 靚咗, FIT咗, 讀書仲好咗, 仲拿第一添.
我做文職, 133磅, 160CM , 用咗簡單又健康既方法!
我用左4個月減左20磅, 改善頭痛,胃痛, 暈車浪,植物曲脹, 越來越fit!面色仲好過以前!
網站可以增肥, 減肥, 改善身形, 健康, 體重控制,
美容護膚, http://www.healthcometrue.com/life
[[有營養顧問免費跟進^^ ]]
TEL: 93227176 阿紅
2008-10-31 3:10 am
(1) For n = k+1.
(1/3)k(k+1)(k+2) + (k+1)(k+2) = (k+1)(k+2)[k/3 + 1] = (1/3)(k+1)(k+2)(k+3)
= (1/3)(k+1)[(k+1) +1][(k+2) + 1].
(2)
1 x 3 + 2 x 4 + 3 x 5 +.......+ 50 x 52
= 1x (2 +1) + 2 x (3 + 1) + 3 x (4 + 1) +.......+ 50 x (51 + 1)
= 1 x 2 +1 + 2 x 3 + 2 + 3 x 4 + 3 +.......+ 50 x 51 + 50
= (1 x 2 + 2 x 3 + 3 x 4 +.......+ 50 x 51) + ( 1 + 2 + 3 + 4 +.....+ 50)
= (1/3)(50)(51)(52) + (1/2)(50)(51)
= 2550[52/3 + 1/2]
= 2550(107)6
=45475.
(1/3)k(k+1)(k+2) + (k+1)(k+2) = (k+1)(k+2)[k/3 + 1] = (1/3)(k+1)(k+2)(k+3)
= (1/3)(k+1)[(k+1) +1][(k+2) + 1].
(2)
1 x 3 + 2 x 4 + 3 x 5 +.......+ 50 x 52
= 1x (2 +1) + 2 x (3 + 1) + 3 x (4 + 1) +.......+ 50 x (51 + 1)
= 1 x 2 +1 + 2 x 3 + 2 + 3 x 4 + 3 +.......+ 50 x 51 + 50
= (1 x 2 + 2 x 3 + 3 x 4 +.......+ 50 x 51) + ( 1 + 2 + 3 + 4 +.....+ 50)
= (1/3)(50)(51)(52) + (1/2)(50)(51)
= 2550[52/3 + 1/2]
= 2550(107)6
=45475.
收錄日期: 2021-04-19 12:46:04
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081030000051KK01359