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二分之1+6分之1+10二分之一省略号一直加到九十分之...

1/2+1/6+1/12+....+1/90 =1-1/2+1/2-1/3+1/3-1/4+......+1/9-1/10 =1-1/10 =9/10 =10分之9

欧拉公式:1+1/2+1/3+……+1/n=ln(n)+C,C为欧拉常数 数值是0.5772 1/2 + 3/4 + 5/6 + 7/8 + ...... + 199/200 = (1-1/2) + (1-1/4) + (1-1/6) + (1-1/8) + ......+ (1-1/200) = (1+1+1+1+.....1) - (1/2+1/4+1/6+1/8+ ...... 1/200) = 100 - 1/2(...

解:由题意知:2/3+2/9+2/17+2/81+............. 是求首项为a1=2/3,公比为q=1/3的无穷等比数列各项的和 所以 由无穷递缩等比数列的求和公式.S=a1/(1-q)可得: 2/3+2/9+2/17+2/81+............. =(2/3)/[1-(1/3)] =(2/3)/(2/3) =1。

=1/2-[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/9-1/10)] =1/2-[1/2-1/10] =1/10

(1-1/2)×(1-1/3)×(1-1/4)×……×(1-1/999)×(1-1/1000) =1/2×2/3×3/4×……×998/999×999/1000 =1/1000

裂项法: 5/6-7/12+9/20-11/30+……+37/(18×19)-39/(19×20) =1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+……+1/18+1/19-1/19-1/20 =1/2-1/20 =9/20

(1-1/2)X(2-2/3)X(3-3/4)X......X(9-9/10) =(1/2)X(4/3)X(9/4)X(16/5)X(25/6)X(36/7)X(49/8)X(64/9)X(81/10) =2X3X4X5X6X7X8X9/10 =3X4X6X7X8X9 =36288

3/19+4/19+5/19+6/19+……+9/19+10/19 =(3/19+10/19)×8÷2 =13/19×4 =52/19 =2又14/19

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