Question

依照规律计算:1/1×3+1/3×5+1/5×7+...+1/2013×2015

帮忙谢谢

Answer 1

1/1×3+1/3×5+1/5×7+...+1/2013×2015
=2×(1/1×3+1/3×5+1/5×7+...+1/2013×2015)÷2
=(2/1×3+2/3×5+2/5×7+...+2/2013×2015)÷2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+......+1/2011-1/2013+1/2013-1/2015)÷2
=(1-1/2015)÷2
=2014/2015÷2
=1007/2015

Answer 2

1/1×3+1/3×5+1/5×7+...+1/2013×2015
=0.5【(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+...........+(1/2013-1/2015)】
=0.5[1/3-1/2015]
剩下的自己算

其中
1/[(2n-1)(2n+1)]
=0.5[1/(2n-1)-1/(2n+1)]