1 3 5 7 9 11 13 15加30
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/24 15:53:42
1/6+1/12+1/20+1/30+1/42+1/56+1/72=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9=1/2-1/9=7/
1/2-1/3+1/3-1/4……+1/9-1/10=1/2-1/10=2/5
1/6=(1/2)*(1/3),1/12=(1/3)*(1/4),1/20=(1/4)*(1/5),1/30=(1/5)*(1/6),1/42=(1/6)*(1/7),1/56=(1/7)*(1/8)
仔细看就会发现1/6=1/2-1/3,1/12=1/3-1/4...它们是有规律的原式=1+12+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1
1/6+1/12+1/72+1/30+1/20+1/42+1/56=(12+6+1)/72+(3+2)/60+(4+3)/168=19/72+1/12+1/24=(19+6+3)/72=28/72=7
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=1-1
1/2+1/6+1/12+1/20+1/30+1/42=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)=1-1/7=6/7
=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/
1/2+1/2-1/3+1/3-1/4+1/4-1/5+.-.-1/10=9/10求最佳!
1/2+1/6+1/12+1/20+1/30+1/42=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)=1-1/2+1/2-1/3+
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1-1/7=6/7
25/61
解题思路:用裂项法进行计算.解题过程:
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9=1/
二分之一加6分之一加12分之一加20分之一加30分之一加42分之一=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7(裂项相消)=1-1/76/7
=1/1×2+1/2×3+1/3×4+……+1/2010×2011=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011=1-1/2011=2010/2011
没有这种物质,硫酸是二元酸,不可能有二氢盐.磷酸是三元酸,磷酸二氢铵的化学式是NH4H2PO4
二分之一加6分之一加12分之一加20分之一加30分之一加42分之一加五十六分之一=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=1-1/8