数学简便计算题(平方差公式)一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 16:41:20
![数学简便计算题(平方差公式)一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15](/uploads/image/z/755883-27-3.jpg?t=%E6%95%B0%E5%AD%A6%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E9%A2%98%EF%BC%88%E5%B9%B3%E6%96%B9%E5%B7%AE%E5%85%AC%E5%BC%8F%EF%BC%89%E4%B8%80%E3%80%81%281-1%2F2%26%23178%3B%29%281-1%2F3%26%23178%3B%29%281-1%2F4%26%23178%3B%29%E2%80%A6%E2%80%A6%281-1%2F99%26%23178%3B%29%281-1%2F100%26%23178%3B%29%E4%BA%8C%E3%80%81%281%2B1%2F2%29%281%2B1%2F2%26%23178%3B%29%281%2B1%2F2%26%238308%3B%29%281%2B2%5E8%29%2B1%2F2%5E15)
数学简便计算题(平方差公式)一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
数学简便计算题(平方差公式)
一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
数学简便计算题(平方差公式)一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
一、(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/99²)(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/100)(1+1/100)
=1/2x3/2x2/3x...x99/100x101/100
=1/2x101/100
=101/200
二、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2)、(1+1/2)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=2*(1-1/2²)(1+1/2²)(1+1/2⁴)(1+2^8)+1/2^15
=.
=2*(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2
如追加其它问题,采纳本题后点击想我求助,
(a+b)(a-b)=a的平方-b的平方
给个思路你
(1)
[1-(1/2)²][1-(1/3)²].......[1-(1/99)²][1-(1/100)²]
1. (1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1-1/99)(1+1/100)(1-1/100)
=3/2×1/2×4/3×2/3×5/4×3/4……×98/99×101/100×99/100
=1/2×101/100= 101/200
2.