原式=1/(1*3）+1/(3*5)+1/(5*7)+……+1/(99*101)
=(3-1)/(3*1)+(5-3)/(5*3)+(7-5)/(7*5)……+(101-99)/(101*99)
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)……+(1/99-1/101)]
=1/2*(1-1/101)
=(1/2)*(100/101)
=50/101
不明白的地方可追问,这道题用的是裂项求和的思想
1/3+1/15+1/35+1/63+……+1/9999=?
原式=1/(1*3）+1/(3*5)+1/(5*7)+……+1/(99*101)
=(3-1)/(3*1)+(5-3)/(5*3)+(7-5)/(7*5)……+(101-99)/(101*99)
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)……+(1/99-1/101)]
=1/2*(1-1/101)
=(1/2)*(100/101)
=50/101
不明白的地方可追问,这道题用的是裂项求和的思想