3+13/6+37/12+81/20+151/30+253/42+393/56+577/72+811/90怎样简算?

3+13/6+37/12+81/20+151/30+253/42+393/56+577/72+811/90
=3+(2+1/6)+(3+1/12)+(4+1/20)+(5+1/30)+(6+1/42)+(7+1/56)+(8+1/72)+(9+1/90)
=2+(1+2+3+...+9)+(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=2+45+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=47+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+....+(1/8-1/9)+(1/9-1/10)
=47+1/2-1/10
=47+2/5

3+13/6+37/12+81/20+151/30+253/42+393/56+577/72+811/90=3+2+1/6+3+1/12+4+1/20+5+1/30+6+1/42+7+1/56+8+1/72+9+1/90=3+2+3+4+5+6+7+8+9+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=3+(2+9)*8/2+1/2*3+1/3*4+1/4*5+1/...