Question

1/1*2*3+1/2*3*4+1/3*4*5+.......1/48*49*50=?

数学记算题

Answer 1

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，值不变 所以，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