观察下列等式,1+2+3=6=(1+3)*3/2 1+2+3+4=10=(1+4)*4/2 1+2+3+4+5=15=(1+5)*5(1)1+2+3+...+n=________.(2)请利用上面的规律求2+3+...+1000的结果
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![观察下列等式,1+2+3=6=(1+3)*3/2 1+2+3+4=10=(1+4)*4/2 1+2+3+4+5=15=(1+5)*5(1)1+2+3+...+n=________.(2)请利用上面的规律求2+3+...+1000的结果](/uploads/image/z/3982454-62-4.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%2C1%2B2%2B3%3D6%3D%281%2B3%29%2A3%2F2+1%2B2%2B3%2B4%3D10%3D%281%2B4%29%2A4%2F2+1%2B2%2B3%2B4%2B5%3D15%3D%281%2B5%29%2A5%EF%BC%881%EF%BC%891%2B2%2B3%2B...%2Bn%3D________.%EF%BC%882%EF%BC%89%E8%AF%B7%E5%88%A9%E7%94%A8%E4%B8%8A%E9%9D%A2%E7%9A%84%E8%A7%84%E5%BE%8B%E6%B1%822%2B3%2B...%2B1000%E7%9A%84%E7%BB%93%E6%9E%9C)
观察下列等式,1+2+3=6=(1+3)*3/2 1+2+3+4=10=(1+4)*4/2 1+2+3+4+5=15=(1+5)*5(1)1+2+3+...+n=________.(2)请利用上面的规律求2+3+...+1000的结果
观察下列等式,1+2+3=6=(1+3)*3/2 1+2+3+4=10=(1+4)*4/2 1+2+3+4+5=15=(1+5)*5
(1)1+2+3+...+n=________.
(2)请利用上面的规律求2+3+...+1000的结果
观察下列等式,1+2+3=6=(1+3)*3/2 1+2+3+4=10=(1+4)*4/2 1+2+3+4+5=15=(1+5)*5(1)1+2+3+...+n=________.(2)请利用上面的规律求2+3+...+1000的结果
答:
1+2+3+...+n=(1+n)*n/2
2+3+...+1000=(2+1000)*999/2=501*999=501*1000-501
=500499