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

    
[tex]\displaystyle n = numarul termenilor = 104 - 47 + 1 = 58\\ \text{Rezolvam prima inegalitate} \\ \\ \frac{1}{47} + \frac{1}{48} + \frac{1}{49}+ .. + \frac{1}{104} \ \textgreater \ \frac{1}{104}+\frac{1}{104}+...+\frac{1}{104} = \frac{58}{104} = \frac{29}{52} \\ \\ Rezolvam a 2-a inegalitate: \\ \\ \frac{1}{47} + \frac{1}{48} + \frac{1}{49}+ .. + \frac{1}{104} \ \textless \ \frac{1}{47}+\frac{1}{47}+...+\frac{1}{47} = \frac{58}{47} = 1\frac{11}{47} \\ \\ [/tex]