列项公式知：
1/n(n+1)+1/(n+1)(n+2)＋1/(n+2)(n+3)+1/(n+3)(n+4)+....+1/(n+98)(n+99)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+...+1/(n+98)-1/(n+99)
=1/n-1/(n+99)
=99/n(n+99)
根据已知得，n=1，代入公式
99/1x（1+99）=99/100
1/n(n+1)+1/(n+1)(n+2)＋1/(n+2)(n+3)+1/(n+3)(n+4)+....+1/(n+98)(n+99)
=1/n-1/(n+1)+1/(n+1)-1/(n+2)+...+1/(n+98)-1/(n+99)
=1/n-1/(n+99)
=99/n(n+99)
根据已知得，n=1，代入公式
99/1x（1+99）=99/100
