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

1 intreg si 11/47 = 58/47

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

nr termeni   104-47+1=58

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

⇒S >29/52

(1/47 +1/48+1/49 +.......+1/104)<1/47+1/147+....+1/47<58/47<1 intreg 11/47

⇒S <  1 intreg si 11/47