在平面上画出100条直线,这些直线最多可把平面分成多少个区域
人气:383 ℃ 时间:2019-08-19 04:34:28
解答
5051
n条直线可以将平面分割成2n+(n-2)+(n-3)+.+1块区域:则
1根线可分割成2×1=2块区域;
2根线可分割成2×2=4块区域;
3根线可分割成2×3+1=7块区域;
4根线可分割成2×4+2+1=11块区域;
5根线可分割成2×5+3+2+1=16块区域;
6根线可分割成2×6+4+3+2+1=22块区域;
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