1³+2³=1+8=9,而(1+2)²=9 ∴1³+2³=(1+2)²;1³+2³+3³=36,而(1=2+3)²=36;∴1³+2³+3³=(1+2+3)²1³+2³+3³+4=100,而(1+2+3+4)²=100∴1³+2
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 06:19:14
![1³+2³=1+8=9,而(1+2)²=9 ∴1³+2³=(1+2)²;1³+2³+3³=36,而(1=2+3)²=36;∴1³+2³+3³=(1+2+3)²1³+2³+3³+4=100,而(1+2+3+4)²=100∴1³+2](/uploads/image/z/603084-12-4.jpg?t=1%26%23179%3B%2B2%26%23179%3B%3D1%2B8%3D9%2C%E8%80%8C%EF%BC%881%2B2%EF%BC%89%26%23178%3B%3D9+%E2%88%B41%26%23179%3B%2B2%26%23179%3B%3D%EF%BC%881%2B2%EF%BC%89%26%23178%3B%EF%BC%9B1%26%23179%3B%2B2%26%23179%3B%2B3%26%23179%3B%3D36%EF%BC%8C%E8%80%8C%EF%BC%881%3D2%2B3%EF%BC%89%26%23178%3B%3D36%EF%BC%9B%E2%88%B41%26%23179%3B%2B2%26%23179%3B%2B3%26%23179%3B%3D%EF%BC%881%2B2%2B3%EF%BC%89%26%23178%3B1%26%23179%3B%2B2%26%23179%3B%2B3%26%23179%3B%2B4%3D100%2C%E8%80%8C%EF%BC%881%2B2%2B3%2B4%EF%BC%89%26%23178%3B%3D100%E2%88%B41%26%23179%3B%2B2%26%231)
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1³+2³=1+8=9,而(1+2)²=9 ∴1³+2³=(1+2)²;1³+2³+3³=36,而(1=2+3)²=36;∴1³+2³+3³=(1+2+3)²1³+2³+3³+4=100,而(1+2+3+4)²=100∴1³+2
1³+2³=1+8=9,而(1+2)²=9 ∴1³+2³=(1+2)²;
1³+2³+3³=36,而(1=2+3)²=36;
∴1³+2³+3³=(1+2+3)²
1³+2³+3³+4=100,而(1+2+3+4)²=100
∴1³+2³+3³+4=(1+2+3+4)²;
...
∴ 1³+2³+3³+4+5³=( )²___________。
根据以上规律填空:1³+2³+3³+4³+5³+...+n³( )²=[ ]²
猜想2^3+13^3+【14^3】15 ^3=
1³+2³=1+8=9,而(1+2)²=9 ∴1³+2³=(1+2)²;1³+2³+3³=36,而(1=2+3)²=36;∴1³+2³+3³=(1+2+3)²1³+2³+3³+4=100,而(1+2+3+4)²=100∴1³+2
根据以上规律填空:1³+2³+3³+4³+5³+...+n³=(1+2+3+……+n )²=[ n(1+n)/2 ]²
猜想2^3+3^3+……14^3+15 ^3=(1+2+3+……+14+15)²-1
=[ 15×(1+15)/2 ]²-1
=120 ²-1
=14399