简便计算2/(13)+2/(53)+2/(57)+2/(9799)

题目详情

简便计算
2/(1*3)+2/(5*3)+2/(5*7)+2/(97*99)

▼优质解答

答案和解析

2/(1*3)+2/(5*3)+2/(5*7)+...+2/(97*99)
=2*1/2(1-1/3+1/3+1/5-1/7+...+1/97-1/99)
=1-1/99
=98/99

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简便计算2/(1*3)+2/(5*3)+2/(5*7)+2/(97*99)