计算1/{a（a+1）}+1/{（a+1)(a+1)}+{(a+2)(a+3)}+.+1/{(a+2005)(a+2006))}答好了,好大的诱惑哦!

Question

计算1/{a（a+1）}+1/{（a+1)(a+1)}+{(a+2)(a+3)}+.+1/{(a+2005)(a+2006))}
答好了,好大的诱惑哦!

Answer 1

1/{a（a+1）}+1/{（a+1)(a+1)}+{(a+2)(a+3)}+.+1/{(a+2005)(a+2006))}
=1/a-1/(a+1）+1/（a+1)-1/(a+1)}++1/(a+2)-1/(a+3)+.+1/(a+2005)-1/(a+2006))
=1/a-1/(a+2006))
=2006/[a(a+2006)]