Re: [中學] 國中數學
※ 引述《newperson (123456)》之銘言：
: 1+2+3+...+k為一完全平方數N^2
: 若N<100，則k可能値=? ans:1,8,49
: 請教這題 感恩~
k(k+1)
----- = N^2, N<100 => 可知 k 須為某一平方數的2倍, k+1 or k-1 也是平方數
2
k = 2* 1^2 => k-1 = 1^2
k = 2* 2^2 => k+1 = 3^2
k = 2* 3^2 => k-1 = 17, k+1 =19 (皆不為平方數)
k = 2* 4^2 => k-1 = 31, k+1 =32 (皆不為平方數)
k = 2* 5^2 => k-1 = 7^2
k = 2* 6^2 => k-1 = 71, k+1 =73 (皆不為平方數)
k = 2* 7^2 => k-1 = 37, k+1 =99 (皆不為平方數)
k = 2* 8^2 => k-1 = 127, k+1 =129 (皆不為平方數)
k = 2* 9^2 => k-1 = 161 => k(k+1)/2 = (114.2)^2 超過100
所以 k = 1 or 8 or 49 N = 1 or 6 or 35
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