答:
分数的裂项知识:
5/(2*7)+5/(7*12)+5/(12*17)+…+5/(97*102)
=1/2-1/7+1/7-1/12+1/12-1/17+...+1/97-1/102
=1/2-1/102
=51/102-1/102
=50/102
=25/51
非常感谢,能再教一题吗?1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+…+20=?
1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+…+20=分母是自然数列之和第n项的分母是1+2+3+...+n+1=(1+n+1)*(n+1)/2=(n+1)(n+2)/2所以:第n项是2/[(n+1)(n+2)]=2*[1/(n+1)-1/(n+2)]所给等式共有20-1=19项,n=19所以:1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+…+20=2*(1/2-1/3+1/3-1/4+....+1/20-1/21)=2*(1/2-1/21)=1-2/21=19/21