Question

解方程.x/1×3+x/2×4+x/3×5+…+x/98×100=14651

Answer 1

因为1/n(n+2)=(1/n-1/(n+2)]/2,所以

x/(1*3)+x/(2*4)+x/(3*5)+...+x/(98*100)=14651

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

=x(1/1+1/2-1/99-1/100)/2=14651

x(14651/9900)/2=14651

x=9900*2=19800