Question

1、1/(1*2*3）+1/(2*3*4)+1/(3*4*5)…………+1/(99*100*101)

Answer 1

1/(1*2)*1/3+.+1/(99*100)*1/101

(1/1-1/2)*1/3+.+(1/99-1/100)*1/101

1/1*1/3+.1/99*1/101-(1/2*1/3+.1/100*1/101)

1/2*(1/1-1/3+.1/99-1/101)-(1/2-1/101)

1/2(1/1+1/2+1/3+1/4+.+1/98+1/99-1/3-1/4-1/5-.-1/100-1/101)-(1/2-1/101)

1/2(1/1+1/2-1/100-1/101)-1/2+1/101

1/4-1/200+1/2*(1/101)

第二题有错吧?分母上被减项应为偶数,99是奇数呵!