2/1X3+2/3X5+2/5X7+...+2/97X99
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![2/1X3+2/3X5+2/5X7+...+2/97X99](/uploads/image/z/8593294-22-4.jpg?t=2%2F1X3%2B2%2F3X5%2B2%2F5X7%2B...%2B2%2F97X99)
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2/1X3+2/3X5+2/5X7+...+2/97X99
2/1X3+2/3X5+2/5X7+...+2/97X99
2/1X3+2/3X5+2/5X7+...+2/97X99
原式=2-2/3+3/2-2/5+……2/97-2/99
=2-2/99
=196/99
自己约
1/1-1/3+1/3-1/5+..........+1/97-1/99=1-1/99=98/99
2/i(i+2)= 1/i-1/(i+2)
所以 原式=1-1/3+1/3-1/5+...+1/97-1/99=1-1/99=98/99