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a1=1/1*3,a2=1/3*5,a3=1/5*7,a4=1/7*9.求a1+a2+a3+a4+.a100d的值
题目详情
a1=1/1*3,a2=1/3*5,a3=1/5*7,a4=1/7*9.求a1+a2+a3+a4+.a100d的值
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答案和解析
a1+a2+a3+a4+.a100
=1/1×3+1/3×5+.+1/199×201
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/199-1/201)
=(1/2)(200/201)
=100/201
=1/1×3+1/3×5+.+1/199×201
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/199-1/201)
=(1/2)(200/201)
=100/201
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