（1）分母太乱,看不懂
(2)总结原式规律得下式：
1/n + 1/[n(n+3)] + 1/[(n+3)(n+3*2)] + ……+ 1/{(n+3a)[n+3(a+1)]}
= 1/n + (1/3){[1/n - 1/(n+3)] + [1/(n+3) - 1/(n+3*2)] +……+ [1/(n+3a) - 1/(n+3a+3)]}
= 1/n + (1/3)[1/n - 1/(n+3a+3)]
题中n = 4 ,(n+3a+3) = 100,所以：原式 = 1/4 + (1/3)[1/4 - 1/100] = 33/100
（3）总结原式规律得下式：
1/n + 1/[n(n+2)] + 1/[(n+2)(n+2*2)] + ……+ 1/{(n+2a)[n+2(a+1)]}
= 1/n + (1/2){[1/n - 1/(n+2)] + [1/(n+2) - 1/(n+2*2)] +……+ [1/(n+2a) - 1/(n+2a+2)]}
= 1/n + (1/2)[1/n - 1/(n+2a+2)]
题中n = 3 ,(n+2a+2) = 101,所以：原式 = 1/3 + (1/2)[1/3 - 1/101] = 50/101
（4）原式 = 21 - 4[1/3 + 1/(3×5) + 1/(5×7) + 1/(7×9) + 1/(9×11) + 1/(11×13) + 1/(13×15)+
1/(15×17)]
= 21 - 4[1/3 +(1/2 )(1/3 - 1/255)] (注：此式的推导过程参见（3）题的题解）
= 4847/255
(5) 6天
设五个小队每天完成的工作量分别为a,b,c,d,e
则 a+b+c = 1/12 ①
a+c+e = 1/7 ②
b+d+e = 1/8 ③
a+c+d = 1/42 ④
2*①+2*②+4*③+2*④得：6(a+b+c+d+e)=1 即a+b+c+d+e = 1/6
所以五个队合干需要6天完成.
（6）20天
设甲做了D天,由题可知乙做了3D天,丙做了6D天.得出下式：
D*(1/12) + 3D*(1/18) + 6D*(1/24) = 1
解得D = 2,共做了D+3D+6D = 10D = 20天.
