简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 06:41:54
简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7)

简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7)
简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7)

简便运算 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/7+1/9)*(1/3+1/5+1/7)

设 a = 1+1/3+1/5+1/7+1/9,则
原式
= (a-1/9)(a-1) - a(a-1-1/9)
= a²-10a/9 +1/9 -a²+10a/9
= 1/9
 
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