作业帮计算\frac{1}{a(a+1)}加\frac{1}{(a+1)(a-1)}加\frac{1}{(a+2)(a+3)}+……+\frac{1}{(a+2012)(a+2013)}
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 01:47:47
计算\frac{1}{a(a+1)}加\frac{1}{(a+1)(a-1)}加\frac{1}{(a+2)(a+3)}+……+\frac{1}{(a+2012)(a+2013)}
计算\frac{1}{a(a+1)}加\frac{1}{(a+1)(a-1)}加\frac{1}{(a+2)(a+3)}+……+\frac{1}{(a+2012)(a+2013)}
计算\frac{1}{a(a+1)}加\frac{1}{(a+1)(a-1)}加\frac{1}{(a+2)(a+3)}+……+\frac{1}{(a+2012)(a+2013)}
1/{a(a+1)}+1/{(a+1)(a+2)+1/{(a+2)(a+3)}+……+1/{(a+2012)(a+2013)}
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/{(a+2)-1/(a+3)+……+1/(a+2012)-1/(a+2013)
=1/a-1/(a+2013)
=2012/{a(a+2013)}
1/{a(a+1)}+1/{(a+1)(a+2)+1/{(a+2)(a+3)}+……+1/{(a+2012)(a+2013)}
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/{(a+2)-1/(a+3)+……+1/(a+2012)-1/(a+2013)
=1/a-1/(a+2013)
=2012/{a(a+2013)}