用提公因式法,求2002+2001×2002²+……+2001×2002²ººº的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 23:56:43
![用提公因式法,求2002+2001×2002²+……+2001×2002²ººº的值](/uploads/image/z/5371838-62-8.jpg?t=%E7%94%A8%E6%8F%90%E5%85%AC%E5%9B%A0%E5%BC%8F%E6%B3%95%2C%E6%B1%822002%EF%BC%8B2001%C3%972002%26%23178%3B%EF%BC%8B%E2%80%A6%E2%80%A6%EF%BC%8B2001%C3%972002%26%23178%3B%26%23186%3B%26%23186%3B%26%23186%3B%E7%9A%84%E5%80%BC)
用提公因式法,求2002+2001×2002²+……+2001×2002²ººº的值
用提公因式法,求2002+2001×2002²+……+2001×2002²ººº的值
用提公因式法,求2002+2001×2002²+……+2001×2002²ººº的值
2002+2001×2002²+……+2001×2002²ººº
=2002+2001×(2002^2+……+2002^2000)
=2002+2001×(1+2002+2002^2+……+2002^2000-2003)
=2002+2001×((1-2002^1999)/(1-2002)-2003)
=2002+2002^1999-1-2001×2003
=2002+2002^1999-1-(2002-1)×(2002+1)
=2002+2002^1999-1-2002^2+1
=2002+2002^1999-2002^2
=2002^1999-2001×2002
额