1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49+51)的简便运算
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1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49+51)的简便运算
![1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49+51)的简便运算](/uploads/image/z/189050-50-0.jpg?t=1%2F%EF%BC%881%2A3%EF%BC%89%2B1%2F%EF%BC%883%2A5%EF%BC%89%2B1%2F%EF%BC%885%2A7%EF%BC%89%2B.%2B1%2F%EF%BC%8849%2B51%EF%BC%89%E7%9A%84%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97)
1/(1*3)+1/(3*5)+1/(5*7)+.+1/(49*51)
=(1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51)/2
=(1-1/51)/2
=25/51
=(1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51)/2
=(1-1/51)/2
=25/51
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