Question

Demonstrati ca 29 supra 52 < 1 supra 47 +1 supra 48 + 1 supra 49 + .... + 1 supra 104 < 1 intreg si 11 supra 47

Answer 1

29/52 < (1/47 +1/48+1/49 +.......+1/104) < 58/47 

1/47 ≤ 1/47  1/48<1/47  1/49 < 1/47 ......1/104 <1/47   S=1/47+1/48+....1/104 ⇒ S < 1/47 × 58 ⇒   S <  58 / 47  

1/47 > 1/104   1/48>1/104    1/49 >1/104 .....1/104 ≥1/104⇒ S=1/104 ·58 S= 29/52 ⇒ S>29/52