1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••••1\(99*99-1)求和
问题描述：
1\(7*7-1)+1\(9*9-1)+1\(11*11-1)+••••••1\(99*99-1)求和
答
原式=1/(7-1)(7+1)+1/(9-1)(9+1)+...+1/(99-1)(99+1)
=1/6x8+1/8x10+...+1/98x100
=1/2[1/6-1/8]+1/2[1/8-1/10]+...+1/2[1/98-1/100]
=1/2[1/6-1/100]
=1/2*47/300
=47/600
答
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