1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••
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1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••••1\(99*99-1)求和
![1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••](/uploads/image/z/15928009-25-9.jpg?t=1%5C%287%2A7-1%29%2B1%5C%289%2A9-1%29%2B1%5C%2811%2A11-1%29%2B%26%238226%3B%26%238226%3B%26%238226%3B%26%238226%3B)
简便计算
1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••••1\(99*99-1)
=1/(7-1)(7+1)+1/(9-1)((+1)+1/(11-1)(11+1)+...+1/(99-1)(99+1)
=1/6x8+1/8x10+1/10x12+...+1/98x100
=1/2(1/6-1/8)+1/2(1/8-1/10)+1/2(1/10-1/12)+..+1/2(1/98-1/100)
=1/2(1/6-1/100)
=1/2(50/300-3/300)
=47/600
1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••••1\(99*99-1)
=1/(7-1)(7+1)+1/(9-1)((+1)+1/(11-1)(11+1)+...+1/(99-1)(99+1)
=1/6x8+1/8x10+1/10x12+...+1/98x100
=1/2(1/6-1/8)+1/2(1/8-1/10)+1/2(1/10-1/12)+..+1/2(1/98-1/100)
=1/2(1/6-1/100)
=1/2(50/300-3/300)
=47/600
计算1+3+5+7+9+11+••••••+20
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1-2-3-4-5-6-7-8-9-10-•••••R
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