巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 01:13:54
![巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)](/uploads/image/z/1168083-27-3.jpg?t=%E5%B7%A7%E7%AE%97%EF%BC%9A%EF%BC%883%2B1%EF%BC%89%EF%BC%883%E7%9A%842%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%883%E7%9A%844%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%883%E7%9A%845%E6%AC%A1%E6%96%B9%2B1%EF%BC%89......%EF%BC%883%E7%9A%842n%E6%AC%A1%E6%96%B9%2B1%EF%BC%89)
巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
题目应该是这样的:
原式的=
2(3+1)(3^2 +1)(3^4 +1)(3^8 +1).(3^2n+1)/2
=(3-1)(3+1)(3^2 +1)(3^4 +1).(3^2n+1)/2
=(3^2-1)(3^2+1)(3^4+1).(3^2n+1)/2
=(3^4-1)(3^4+1)(3^8+1).(3^2n+1)/2
=.
=(3^4n-1)/2
(3+1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=(3²-1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/2
=(3^4-1)(3^4+1)(3^8+1)...(3^2n+1)/2
=(3^2n-1)(3^2n+1)/2
=(3^4n-1)/2