1/34+1/35+1/36+.+1/100>1

1/34+1/35+1/36+.+1/100>1
1/34+1/35+1/36+.+1/100>1

1/34+1/35+1/36+.+1/100>1
1/34>1/40~1/34+1/35+1/36+.+1/40>7/40
1/41+.+1/50>1/5
1/51+.+1/60>1/6
1/61+.+1/70>1/7
1/71+.+1/80>1/8
1/81+.+1/90>1/9
1/91+.+1/100>1/10
1/34+1/35+1/36+.+1/100>24/40+1/6+1/7+1/9=3/5+53/126>(75+53)/126=128/126
故：原不等式成立