计算:2/3+2/15+2/35+2/63+......+2/9603=?
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计算:2/3+2/15+2/35+2/63+......+2/9603=?
![计算:2/3+2/15+2/35+2/63+......+2/9603=?](/uploads/image/z/16684240-40-0.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A2%2F3%2B2%2F15%2B2%2F35%2B2%2F63%2B......%2B2%2F9603%3D%3F)
2/3+2/15+2/35+2/63+……+2/9603
=2/3+2/(3×5)+2/(5×7)+2/(7×9)+……2/(97×99)
=2/3+1/2×(1/3-1/5)+1/2×(1/5-1/7)+1/2×(1/7-1/9)+……1/2×(1/97-1/99)
=2/3+1/2×(1/3-1/5+1/5-1/7+1/7-1/9+……+1/97-1/99)
=2/3+1/2×(1/3-1/99)
=2/3+1/2×32/99
=82/99
=2/3+2/(3×5)+2/(5×7)+2/(7×9)+……2/(97×99)
=2/3+1/2×(1/3-1/5)+1/2×(1/5-1/7)+1/2×(1/7-1/9)+……1/2×(1/97-1/99)
=2/3+1/2×(1/3-1/5+1/5-1/7+1/7-1/9+……+1/97-1/99)
=2/3+1/2×(1/3-1/99)
=2/3+1/2×32/99
=82/99