Bạn xem lời giải của mình nhé:
Giải:
\(S=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\\ \frac{1}{13}< \frac{1}{12}\\ \frac{1}{14}< \frac{1}{12}\\ \frac{1}{15}< \frac{1}{12}\\ \frac{1}{61}< \frac{1}{60}\\ \frac{1}{62}< \frac{1}{60}\\ \frac{1}{63}< \frac{1}{60}\)
\(\Rightarrow\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)< \frac{1}{5}+\left(\frac{1}{12}+\frac{1}{12}+\frac{1}{12}\right)+\left(\frac{1}{60}+\frac{1}{60}+\frac{1}{60}\right)\)
\(\Rightarrow A< \frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3\\ \Rightarrow A< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}\\ \Rightarrow A< \frac{4+5+1}{20}\\ \Rightarrow A< \frac{1}{2}\left(đpcm\right)\)
Chúc bạn học tốt!
Ta có:
\(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)
\(< \frac{1}{5}+\frac{1}{12}+\frac{1}{12}+\frac{1}{12}+\frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{1}{5}+\frac{3}{12}+\frac{3}{60}=\frac{1}{2}\)
Hay \(S< \frac{1}{2}\)
Vậy \(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)
!
S=15+(113+114+115)+(161+162+163)113<112114<112115<112161<160162<160163<160S=15+(113+114+115)+(161+162+163)113<112114<112115<112161<160162<160163<160
⇒15+(113+114+115)+(161+162+163)<15+(112+112+112)+(160+160+160)⇒15+(113+114+115)+(161+162+163)<15+(112+112+112)+(160+160+160)
⇒A<15+112.3+160.3⇒A<15+14+120⇒A<4+5+120⇒A<12(đpcm)
