200*(1/(2*4)+1/(4*6)+1/(6*8)++1/(98*100))=?

200*(1/(2*4)+1/(4*6)+1/(6*8)+...+1/(98*100))=50*(1/(1*2)+1/(2*3)+1/(3*4)+...+1/(49*50))=50*((2-1)/(1*2)+(3-2)/(2*3)+(4-3)/(3*4)+...+(50-49)/(49*50))=50*(2/(1*2)-1/(1*2)+3/(2*3)-2/(2*3)+4/(3*4)-3/(3*4)+...+50/(49*50)-49/(49*50))=50*(1-1/2+1/3-1/3+1/3-1/4+...+1/49-1/50)=50*(1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50)=50*(1-1/50)=50-1=49