观察下列等式,1/1*1=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4.猜想并写出:1/n(n+1)=直间写出下列各式的计算结果:(1)1/1*2+1/2*3+1/3*4+…
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 13:47:00
![观察下列等式,1/1*1=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4.猜想并写出:1/n(n+1)=直间写出下列各式的计算结果:(1)1/1*2+1/2*3+1/3*4+…](/uploads/image/z/8818659-27-9.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%2C1%2F1%2A1%3D1-1%2F2%2C1%2F2%2A3%3D1%2F2-1%2F3%2C1%2F3%2A4%3D1%2F3-1%2F4%2C%E5%B0%86%E4%BB%A5%E4%B8%8A3%E4%B8%AA%E7%AD%89%E5%BC%8F%E4%B8%A4%E8%BE%B9%E5%88%86%E5%88%AB%E7%9B%B8%E5%8A%A0%2C%E5%BE%97%2C1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F4.%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA%EF%BC%9A1%2Fn%EF%BC%88n%2B1%EF%BC%89%3D%E7%9B%B4%E9%97%B4%E5%86%99%E5%87%BA%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E8%AE%A1%E7%AE%97%E7%BB%93%E6%9E%9C%EF%BC%9A%EF%BC%881%291%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B%E2%80%A6)
观察下列等式,1/1*1=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4.猜想并写出:1/n(n+1)=直间写出下列各式的计算结果:(1)1/1*2+1/2*3+1/3*4+…
观察下列等式,1/1*1=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,1/1*2+1/2*3
+1/3*4
=1-1/2+1/2-1/3+1/3-1/4
=1-1/4
=3/4.
猜想并写出:1/n(n+1)=
直间写出下列各式的计算结果:
(1)1/1*2+1/2*3+1/3*4+…+1/2011*2012=
(2)1/1*2+1/2*3+1/3*4+...+1/n(n+1)=
(3)探究并计算:1/2*4+1/4*6+1/6*8+...+1/2012*2012=
求求你们速答,我写作业
观察下列等式,1/1*1=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4.猜想并写出:1/n(n+1)=直间写出下列各式的计算结果:(1)1/1*2+1/2*3+1/3*4+…
观察下列等式,1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,将以上3个等式两边分别相加,得,
1/1*2+1/2*3+1/3*4
=1-1/2+1/2-1/3+1/3-1/4
=1-1/4
=3/4.
猜想并写出:1/n(n+1)=1/n-1/(n+1)
直间写出下列各式的计算结果:
(1)1/1*2+1/2*3+1/3*4+…+1/2011*2012=2011/2012
(2)1/1*2+1/2*3+1/3*4+...+1/n(n+1)=n/(n+1)
(3)探究并计算:
1/2*4+1/4*6+1/6*8+...+1/2010*2012
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2010-1/2012)
=1/2*(1/2-1/2012)
=1/2*1005/2012
=1005/4024