1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/10/06 15:06:05
1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=?
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1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=?
1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=?

1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=?
1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)...1/(199*201)=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9...+1/199-1/201)=100/201

原式=(1-1/3+1/3-1/5+1/5-1/7+……+1/199-1/201)x 1/2
=(1-1/201)x 1/2
=200/201 x 1/2
=100/201

=1/2×(1-1/3+1/3-1/5+……+1/199-1/201)=1/2×(1-1/201)=100/201