1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+.+1/(n+99)+(n+100)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+.1/(n+99)-1/(n+100)
=1/n-1/(n+100)
=100/n(n+100)
1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+.+1/(n+99)+(n+100)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+.1/(n+99)-1/(n+100)
=1/n-1/(n+100)
=100/n(n+100)