1/1*2*3+1/2*3*4+...+1/(48*49*50)
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![1/1*2*3+1/2*3*4+...+1/(48*49*50)](/uploads/image/z/167069-29-9.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B...%2B1%2F%EF%BC%8848%2A49%2A50%EF%BC%89)
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1/1*2*3+1/2*3*4+...+1/(48*49*50)
1/1*2*3+1/2*3*4+...+1/(48*49*50)
1/1*2*3+1/2*3*4+...+1/(48*49*50)
1/(1*2*3 ) +1/(2*3*4 ) + ...+ 1/(48*49*50)
=1/2[1/(1*2)-1/(2*3)]+1/2[1/(2*3)-1/(3*4)] + ...+ 1/2[1/(48*49)-1/(49*50)]
=1/2[1/(1*2)-1/(49*50)]
=306/1225