(1-1/2^2)(1-1/3^2)(1-1/4^2)···(1-1/n^2)···(1-1/100^2)
=(i=2,100)∏(1-1/i^2)
=(i=2,100)∏[(1+1/i)(1-1/i)]
=(i=2,100)∏(1+1/i)×(i=2,100)∏(1-1/i)
=[(3/2)×(4/3)×(5/4)×···×(101/100)]
×[(1/2)×(2/3)×(3/4)×···×(99/100)]
=(101/2)×(1/100)
=101/200
____∏是求積符合,和求和符號(hào)∑是一樣的!用∏,可以節(jié)約很多筆墨,思路清晰,不易出錯(cuò),用它好啊,特別是解決一些比這題更復(fù)雜更龐大的求積問題時(shí),你不想用∏都不行!