1/(1*3)+1/(2*4)+1/(3*5)+……+1/(98*100)+1/(99*101)=?

问题描述:

1/(1*3)+1/(2*4)+1/(3*5)+……+1/(98*100)+1/(99*101)=?

裂项即可,1/(1*3)可写成1/2(1-1/3),1/(2*4)可写成1/2(12-1/4),1/(3*5)1/2(1/3-1/5),依此类推,最后全部裂项即可求解.