要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
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![要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101](/uploads/image/z/669784-40-4.jpg?t=%E8%A6%81%E7%AE%80%E7%AE%97+1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B1%2F3%2A4%2A5%2B...%2B1%2F98%2A99%2A100%2B1%2F99%2A100%2A101)
要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
要简算
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
(4/1*2*3*4+1/1*2*3*4)+(6/3*4*5*6+3/3*4*5*6)+……+(100/97*98*99*100+97/97*98*99*100)+1/99*100*101
=1/2(1/1*2-1/3*4)+1/2(1/3*4-1/5*6)+……+1/2(1/97*98-1/99*100)+1/99*100*101
=1/2(1/1*2-1/3*4+1/3*4-1/5*6+……+1/97*98-1/99*100)+1/99*100*101
=1/2(1/1*2-1/99*100)+1/99*100*101
=1/4-1/99*100*2+1/99*100*101
=1/4-101/99*100*2*101+2/99*100*2*101
=1/4-99/99*100*2*101
=1/4-1/100*101*2
=50*101/200*101-1/200*101
=50*101-1/200*101
=5049/20200