用适当的方法化简计算:(1-2²/1)(1-3²/1)(1-4²/1)...(1-99²/1)(1-100²/1)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 13:13:45
![用适当的方法化简计算:(1-2²/1)(1-3²/1)(1-4²/1)...(1-99²/1)(1-100²/1)](/uploads/image/z/635981-5-1.jpg?t=%E7%94%A8%E9%80%82%E5%BD%93%E7%9A%84%E6%96%B9%E6%B3%95%E5%8C%96%E7%AE%80%E8%AE%A1%E7%AE%97%EF%BC%9A%281-2%26%23178%3B%2F1%29%281-3%26%23178%3B%2F1%29%281-4%26%23178%3B%2F1%29...%EF%BC%881-99%26%23178%3B%2F1%EF%BC%89%EF%BC%881-100%26%23178%3B%2F1%EF%BC%89)
用适当的方法化简计算:(1-2²/1)(1-3²/1)(1-4²/1)...(1-99²/1)(1-100²/1)
用适当的方法化简计算:(1-2²/1)(1-3²/1)(1-4²/1)...(1-99²/1)(1-100²/1)
用适当的方法化简计算:(1-2²/1)(1-3²/1)(1-4²/1)...(1-99²/1)(1-100²/1)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=1/2 × 3/2×2/3 × 4/3×3/4 × 5/4×4/5 × ……× 100/99×99/100 ×101/100
=1/2×101/100
=101/200