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ta co:
2A=2(2 mu 60 +1 /2 mu 61 +1)
2A=2 mu 61 +2 / 2 mu 61 +1
2A=2 mu 61 +1+1/2 mu 61 +1
2A=1+1/2 mu 61 +1
ta co:
2B=2(2 mu 61 +1/2 mu 62 +1)
2B=2 mu 62 +2/2 mu 62+1
2B=2 mu 62 +1+1/2 mu 62 +1
2B=1+1/2 mu 62 +1
mà 1+1/2 mu 61+1>1+1/2 mu 62 +1 nen 2A >2B
vậy A>B
nhớ k đúng cho mk nha
Ta có:
2.A=2 mủ 61 +2/2 mủ 61 +1=1+(2/2 mủ 61 +1)
2.B=2 mủ 62 + 2 /2 mủ 62 +1=1+(2/2 mủ 62 + 1)
vì ... nên 2.A >2.B.Vậy A>B
\(A=\frac{5^{60}+1}{5^{61}+1}\)
\(5A=\frac{5(5^{60}+1)}{5^{61}+1}=\frac{5^{61}+5}{5^{61}+1}=\frac{5^{61}+1+4}{5^{61}+1}=1+\frac{4}{5^{61}+1}\) \((1)\)
\(B=\frac{5^{61}+1}{5^{62}+1}\)
\(5B=\frac{5(5^{61})+1}{5^{62}+1}=\frac{5^{62}+5}{5^{62}+1}=\frac{5^{62}+1+4}{5^{62}+1}=1+\frac{4}{5^{62}+1}\) \((2)\)
Từ 1 và 2 \(\Rightarrow1+\frac{4}{5^{61}+1}>1+\frac{4}{5^{62}+1}\)
\(\Rightarrow5A>5B\)
Hay \(A>B\)
Vậy : ...
\(A=\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)
Ta có :
\(\frac{1}{13}< \frac{1}{12};\frac{1}{14}< \frac{1}{12};\frac{1}{15}< \frac{1}{12}\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{1}{4}\)
\(\frac{1}{61}< \frac{1}{60};\frac{1}{62}< \frac{1}{60};\frac{1}{63}< \frac{1}{60}\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{1}{20}\)
\(\Rightarrow D=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)
Vậy \(D< \frac{1}{2}\)
\(D=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\)
Nhận xét: \(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)
\(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{3}{60}=\frac{1}{20}\)
\(\Rightarrow D< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)
Vậy D < 1/2
S=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)
suy ra S<1/5+1/12.3+1/60.3
S<1/5+1/4+1/20
S<1/2
A = 1/5 + 1/13 + 1/14 + 1/15 + 1/60 + 1/61 + 1/62 + 1/63
Ta có : A = 1/5 + 1/13 + 1/14 + 1/15 + 1/60 + 1/61 + 1/62 + 1/63 < 1/5 + 1/12 + 1/12 + 1/12 + 1/60 + 1/60 + 1/60
= A < 1/5 + 1/4 + 1/20
= A < 1/2
Vậy A < 1/12
* Cách 1 :
Ta có :
\(5A=\frac{5^{61}+5}{5^{61}+1}=\frac{5^{61}+1+4}{5^{61}+1}=\frac{5^{61}+1}{5^{61}+1}+\frac{4}{5^{61}+1}=1+\frac{4}{5^{61}+1}\)
\(5B=\frac{5^{62}+5}{5^{62}+1}=\frac{5^{62}+1+4}{5^{62}+1}=\frac{5^{62}+1}{5^{62}+1}+\frac{4}{5^{62}+1}=1+\frac{4}{5^{62}+1}\)
Vì \(\frac{4}{5^{61}+1}>\frac{4}{5^{62}+1}\) nên \(1+\frac{4}{5^{61}+1}>1+\frac{4}{5^{62}+1}\)
\(\Rightarrow\)\(5A>5B\) hay \(A>B\)
Vậy \(A>B\)
Chúc bạn học tốt ~