1/(1*2)+1/(2*3)+1/(3*4)+.+1/(9998*9999)+1/(9999*10000)
=1-1/2+1/2-1/3+1/3-1/4+.+1/9998-1/9999+1/9999-1/10000
=1-1/10000
=9999/10000
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(9998*9999)+1/(9999*10000)
=1-1/2+1/2-1/3+1/3-1/4+.+1/9998-1/9999+1/9999-1/10000
=1-1/10000
=9999/10000