3\1+8\1+15\1...+120\1怎么算

3\1+8\1+15\1...+120\1怎么算
3\1+8\1+15\1...+120\1怎么算

3\1+8\1+15\1...+120\1怎么算
3\1+8\1+15\1...+120\1
=1/2[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+.+(1/9-1/11)+(1/10-1/12)]
=1/2(1+1/2-1/11-1/12) （前面留下2个数1,1/2,对称的最后也会留下2个数,其它抵消）
=175/264

3\1+8\1+15\1...+120\1
=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(10*12)
=(1/1-1/3+1/2-1/4+1/3-1/5+...+1/10-1/12)/2
=(1/1+1/2-1/11-1/12)/2
=(10/11+5/12)/2
=175/264