1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?能不能直接一点啊,直接就把答案给出来,给出来我就给你分嘛,你不给出来我怎么给你分啊?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 22:05:03
![1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?能不能直接一点啊,直接就把答案给出来,给出来我就给你分嘛,你不给出来我怎么给你分啊?](/uploads/image/z/165396-12-6.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B1%2F3%2A4%2A5%7E1%2F48%2A49%2A50%3D%3F%E8%83%BD%E4%B8%8D%E8%83%BD%E7%9B%B4%E6%8E%A5%E4%B8%80%E7%82%B9%E5%95%8A%EF%BC%8C%E7%9B%B4%E6%8E%A5%E5%B0%B1%E6%8A%8A%E7%AD%94%E6%A1%88%E7%BB%99%E5%87%BA%E6%9D%A5%EF%BC%8C%E7%BB%99%E5%87%BA%E6%9D%A5%E6%88%91%E5%B0%B1%E7%BB%99%E4%BD%A0%E5%88%86%E5%98%9B%EF%BC%8C%E4%BD%A0%E4%B8%8D%E7%BB%99%E5%87%BA%E6%9D%A5%E6%88%91%E6%80%8E%E4%B9%88%E7%BB%99%E4%BD%A0%E5%88%86%E5%95%8A%EF%BC%9F)
1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?能不能直接一点啊,直接就把答案给出来,给出来我就给你分嘛,你不给出来我怎么给你分啊?
1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?
能不能直接一点啊,直接就把答案给出来,给出来我就给你分嘛,你不给出来我怎么给你分啊?
1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?能不能直接一点啊,直接就把答案给出来,给出来我就给你分嘛,你不给出来我怎么给你分啊?
1/(k-1)k(k+1)
=1/k(k^2-1)
=k/(k^2-1)-1/k
=1/2(k-1)+1/2(k+1)-1/k
[49>=k>=2]
就按这种思路把每项分解开再求和.
好吧,那就给你算出来吧.
通项
=1/2(k-1)+1/2(k+1)-1/k
=[1/(k-1)+1/(k+1)]/2-1/k
原式
=[1/1+1/3]/2-1/2
+[1/2+1/4]/2-1/3
+[1/3+1/5]/2-1/4
+[1/4+1/6]/2-1/5
...
+[1/46+1/48]/2-1/47
+[1/47+1/49]/2-1/48
+[1/48+1/50]/2-1/49
上式各项同乘以2,整体再除以2,其值不变.
∴原式
={[1/1+1/3]-2/2
+[1/2+1/4]-2/3
+[1/3+1/5]-2/4
+[1/4+1/6]-2/5
...
+[1/46+1/48]-2/47
+[1/47+1/49]-2/48
+[1/48+1/50]-2/49}/2
={1/2-1/49+1/50}/2
=(25*49-50+49)/2*49*50
=1224/4900
=306/1225
1/(k-1)k(k+1) =1/k(k^2-1) =k/(k^2-1)-1/k=1/2(k-1)+1/2(k+1)-1/k [49>=k>=2]
...类推...把每项分解开再求和