1/13+1/35+1/57+1/79+…+1/20012003
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![1/13+1/35+1/57+1/79+…+1/20012003](/uploads/image/z/12878046-54-6.jpg?t=1%2F13%2B1%2F35%2B1%2F57%2B1%2F79%2B%E2%80%A6%2B1%2F20012003)
1/13+1/35+1/57+1/79+…+1/20012003
1/13+1/35+1/57+1/79+…+1/20012003
1/13+1/35+1/57+1/79+…+1/20012003
中间是×
1/1×3=1/2(1-1/3)
1/3×5=1/2(1/3-1/5)
原式=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/2001-1/2003)
=1/2(1-1/2003)
=1001/2003