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小学数学问题找规律

1*2+2*3+3*4+4*5……49*50=?

2024-12-28 08:00:00

推荐回答（2个）

回答1：

1*2=1*1+1
2*3=2*2+2
3*4=3*3+3
。。。。
49*50=49*49+50*50
1*1+2*2+3*3+......+49*49=49*50*99/6=40425
1+2+3+.....+50=1275
40425+1275=41700
(从1开始连续自然数到n的平方之和=n*（n+1)*(2n+1）/6

回答2：

原式=
（2*2-2）+（3*3-3）+......+(50*50-50)

添加一项 1*1-1
可以= 1*1+2*2+3*3+......+50*50 -（1+2+......+50）
1*1+2*2+3*3+......+50*50 根据公式：
1^2+2^2+3^2+....+n^2=n(n+1)(2n+1)/6

=50*（50+1）*（2*50+1）/6 - (1+50)*50/2
=50*51*101/6-51*25
=42925-1275
=41650

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