求数列1*(1/3)+(1/3)*(1/5)+(1/5)*(1/7)+(1/7)*(1/9)+...+(1/99)*(1/101)的值

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求数列1*(1/3)+(1/3)*(1/5)+(1/5)*(1/7)+(1/7)*(1/9)+...+(1/99)*(1/101)的值

求数列1*(1/3)+(1/3)*(1/5)+(1/5)*(1/7)+(1/7)*(1/9)+...+(1/99)*(1/101)的值
求数列1*(1/3)+(1/3)*(1/5)+(1/5)*(1/7)+(1/7)*(1/9)+...+(1/99)*(1/101)的值

求数列1*(1/3)+(1/3)*(1/5)+(1/5)*(1/7)+(1/7)*(1/9)+...+(1/99)*(1/101)的值
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.+(1/99-1/101)/2
=(1-1/3+1/3-1/5+1/5-1/7+.+1/99-1/101)/2
=(1-1/101)/2
=50/101