22+23+24+...+M=1095
請問正整數M的值是多少﹖
送10分題﹕求M的值
2007-03-03 10:29 pm
回答 (5)
2007-03-03 10:35 pm
✔ 最佳答案
[(1+M)*M]/2 -[(1+21)*21]/2=1095(1+M)M-(22)(21)=2190
M^2+M-2652=0
M=51 or -52(rejected)
thus,M=51
2007-03-03 14:37:21 補充：
用到的公式:(首項+尾項)*項數除2eg:1+2+3+4+...+N=(1+N)N/210+11+12+13+....N=(1+N)N/2 -(1+9)9/2
2007-03-03 11:34 pm
22+23+24+...+M=1095
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51
參考: 我
2007-03-03 10:37 pm
22+23+24+...+M=1095
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51 or M=-52 (rejected)
Therefore M=51.
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51 or M=-52 (rejected)
Therefore M=51.
參考: me
2007-03-03 10:36 pm
22+23+24+...+M=1095
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51 or M=-52 (rejected)
Therefore M=51.
2007-03-03 14:50:45 補充：
樓下:抄襲連一隻字也不改動......
(22+M)(M-22+1)/2=1095
(M+22)(M-21)=2190
M²+M-462=2190
M²+M-2652=0
(M-51)(M+52)=0
M=51 or M=-52 (rejected)
Therefore M=51.
2007-03-03 14:50:45 補充：
樓下:抄襲連一隻字也不改動......
2007-03-03 10:33 pm
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收錄日期: 2021-04-23 00:09:25
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070303000051KK02298