3\1+8\1+15\1...+120\1怎么算
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![3\1+8\1+15\1...+120\1怎么算](/uploads/image/z/767416-40-6.jpg?t=3%5C1%2B8%5C1%2B15%5C1...%2B120%5C1%E6%80%8E%E4%B9%88%E7%AE%97)
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