数学题目..会的进~

1.{b/a(a+b}+{c/(a+b)(a+b+c)}+{d/(a+b+c)(a+b+c+d)}
={1/a-1/(a+b)}+{1/(a+b)-1/(a+b+c)}+{1/(a+b+c)-1/(a+b+c+d)}
=1/a-1/(a+b+c+d)
=(b+c+d)/a(a+b+c+d)

2.{2a-b-c/(a-b)(a-c)}+{2b-c-a/(b-c)(b-a)}+{2c-a-b/(c-b)(c-a) }
={[(a-b)+(a-c)]/(a-b)(a-c)}+{[(b-c)+(b-a)]/(b-c)(b-a)}+{[(c-b)+(c-a)]/(c-b)(c-a) }
={1/(a-c)+1/(a-b)}+{1/(b-c)+1/(b-a)}+{1/(c-b)+1/(c-a)}
={1/(a-c)+1/(a-b)}+{1/(b-c)-1/(a-b)}+{-1/(b-c)-1/(a-c)}
=0

3.{2/(x+1)(x+3)}+{2/(x+3)(x+5)}+****+{2/(x+2005)(x+2007)}
={1/(x+1)-1/(x+3)}+{1/(x+3)-1/(x+5)}+...+{1/(x+2005)-1/(x+2007)}
=1/(x+1)-1/(x+2007)
=(x+2007-(x+1))/(x+1)(x+2007)
=2006/(x+1)(x+2007)

这几题的形式都是一样的
1.b/a(a+b)=1/a-1/(a+b)
c/(a+b)(a+b+c)=1/(a+b)-1/(a+b+c)
d/(a+b+c)(a+b+c+d)=1/(a+b+c)-1/(a+b+c+d)
相加，原式=1-1/(a+b+c+d)

2.2a-b-c/(a-b)(a-c)=1/(a-b)+1/(a-c)
其他三个同理，依次计算，再削掉相反的，结果为0

3.2/(x+1)(x+3)=1/(x+1)-1/(x+3)
依次类推，应该会算了吧~

都是裂项相加
1、b/a(a+b)拆